The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer:
A. The y-intercept represents the number of mammals when they were originally counted.
B. The line y = 0 is an asymptote of the graph.
C. The y-intercept.is 75.
D. The y-intercept is 120.
E. The asymptote indicates that the number of mammals counted when the study began was 120.
F. The asymptote indicates that as years pass, the number of mammals will approach 0.
G. The line x = 0 is an asymptote of the graph.
Answers
The y-intercept (0, 120), and the point (55, 17), on the graph of the exponential function of the population of mammals with the population decreasing at 3.5% per year indicates;
A. The y-intercept represents the number of mammals when they were originally counted was 120
B. The line y = 0 is an asymptote of the graph
D. The y-intercept is 120
F. The asymptote indicates that as years pass, the number of mammals will approach 0
What is an asymptote of a graph?An asymptote is a line on a graph that the curve of a graph approaches as the values of the graph increases to infinity.
The points on the graph of the exponential function are;
(0, 120) and (55, 17)
The rate at which the population is decreasing = -3.5%
The output of the graph, y = The number of mammals x years after counting
The key features of the exponential function are;
The y-intercept of the graph is the point x = 0, which corresponds to year 0, or the time when the mammals were originally counted and the y-value at the y-intercept represents the number of mammals when they were counted originally, therefore option A is correct
The coordinates of the y-intercept is (0, 120)
The y-intercept is therefore the point y = 120
Therefore, option D is correct
The general form of the growth exponential function is presented as follows;
f(x) = a·bˣ + k
r = b - 1
b = 1 + r
Therefore;
b = 1 - 0.035 = 0.965
a = The first term = 120
Plugging in the known values from the graph, we get;
f(0) = 120 = a + k
120 = 120 + k
k = 120 - 120 = 0
k = 0 = The asymptote
Therefore, an asymptote is the line y = 0 option B is therefore correct
The number of mammals approach the asymptote, y = 0 as the number of mammals approach infinity
Therefore as the years pass the number of mammals will approach 0, option F is correct
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Related Questions
can someone pls help me
Answers
Answer: AAS
Step-by-step explanation:
Because of the pair of vertical angles, there are two pairs of congruent angles and one pair of congruent sides. This means the triangles are congruent by AAS.
Step A
Let x = Elijah’s age.
x + 4 = James’s age
2(x +4) = Bryan’s age.
Step B
x + x + 4 + 2(x +4) = 80.
Step C 4x + 12 = 80
X = 17
Step D James is 21.
1. Above is a solution to a verbal problem on the Algebra 1 test. Write the word problem that the student was solving.
2. If the equation in step B had been 2(x + 4) = 80, would the wording of the word problem change or stay the same? If it changed, what would it say now?
Answers
1. Elijah is the smallest sibling among his brother who is 4 years older than her and Bryan is the eldest sibling who is twice as James, what is his age of James if the sum of their ages is 80 years?
2. If the equation in step B had been 2(x + 4) = 80, the changed statement would be Bryan is 80 years old.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Here we are converting a numerical expression into a statement.
Given,
Step A
Let x = Elijah’s age.
x + 4 = James’s age
2(x +4) = Bryan’s age.
Step B
x + x + 4 + 2(x +4) = 80.
Step C 4x + 12 = 80
X = 17
Step D James is 21.
The verbal problem to the algebra test can be stated as
Elijah is the smallest sibling among his brother who is 4 years older than her and Bryan is the eldest sibling who is twice as James, what is the age of James if the sum of their ages is 80 years?
If the equation in step B had been 2(x + 4) = 80, the changed statement would be Bryan is 80 years old.
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10x+2y=41
Solve for y and x
Answers
Answer:
{x,y}={25/7,41/7}
Step-by-step explanation:
4x^{2}+16y^{2}-24x+64y+36=0
The center is:
The vertices are:
The foci are:
Answers
For the given equation,4x²−y²−24x−4y+28=0.The center is (h,k)=(3,−2), vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2), foci is (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation of the hyperbola is,
4x²−y²−24x−4y+28=0
Comparing the equation with the standard equation we get,
Center (h,k)=(3,−2)
Vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2)
Foci (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)
Asymptotes y=2x−8 and y=−2x+4
Thus, for the given equation,4x²−y²−24x−4y+28=0.The center is (h,k)=(3,−2), vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2), foci is (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)
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A small theatre's profit, P(x), from selling concert tickets is P(x) = −15x2 + 60x + 30, where x is the number of $2 price increases of each ticket. Use the graph below to answer the question.
Graph of function p of x equals negative 15 x squared plus 60 x plus 30. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 30) and increases to (2, 90) and then decreases through (4.449, 0).
How many price increases maximized the theatre's profit?
0
1.5
2
4.5
Answers
Using the vertex of the quadratic equation, it is found that the profit will be maximized when each ticket price is sold for $2.
What is the vertex of a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Considering the coefficient a, we have;
If a < 0, the vertex is a maximum point.
If a > 0, the vertex is a minimum point.
In this question, the function is modeled as follows, considering x as the price divided by $2.
P(x) = -15x² + 60x + 30.
The coefficients are a = -15 < 0, b = 60, c = 30, therefore the x-value of the vertex is given by:
V = -b/2a
V = -60/2(-15)
V = -60/-30
V = 2
Hence, the profit will be maximized when each ticket price is sold for $2.
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This is a scale drawing of an apartment. The actual apartment has a perimeter of 160 ft. Draw another scale drawing of the apartment using the scale 20 ft to 1 unit from the apartment to the drawing Explain your reasoning
pls help someone
Answers
According to the scale factor, When the scale is changed to 20 feet to 1 unit, then the drawing would be exactly the same shape, here only each side would have half the original drawing units.
Scale factor:
The ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller) is known as scale factor.
Given,
This is a scale drawing of an apartment. The actual apartment has a perimeter of 160 ft.
Here we need to find the reason for the scale drawing of the apartment using the scale 20 feet to 1 unit from the apartment
Here we know that the actual apartment has a perimeter of 160 ft.
And we have to draw another scale drawing of the apartment using the scale 20 feet to 1 unit from the apartment to the drawing.
So, as per the given details, the perimeter lies along the edges of squares and we count 16 sides of squares as we work around the perimeter, this means that each square is calculated as,
=> 160 / 16 = 10 feet on a side.
Therefore, 10 feet in real life plots to 1 unit on the drawing
Therefore, if we change the scale to 20 feet to 1 unit , then the drawing would be exactly the same shape, only each side would have half the original drawing units.
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Given f(x) = x³ + kx + 3, and x + 3 is a factor of f(x), then what is the value of
k?
Answers
If (x + 3) is a factor of f(x) = x³ + kx + 3 , then the value of k is -8 .
In the question ,
it is given that ,
the function is f(x) = x³ + kx + 3 ,
and also given that (x+3) is a factor of f(x) , that means
x + 3 = 0
x = -3
x = -3 should satisfy the function ,
So , substituting x = -3 in the function f(x) = x³ + kx + 3,
we get
f(-3) = (-3)³ + k(-3) + 3 = 0
-27 -3k + 3 = 0
-3k - 24 = 0
-3k = 24
k = 24/(-3)
k = -8
Therefore , If (x + 3) is a factor of f(x) = x³ + kx + 3 , then the value of k is -8 .
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The bookshop received a shipment of identification books. 1/3 of them were bird books, 1/2 of the rest of the books
were about plants, and 1/4 of the remaining books were mammal books. The 12 books that were left were insect
books. How many books were in the shipment?
Answers
Answer:
48
Step-by-step explanation:
1/3+(1/2*2/3)+(1/4*1/3)=3/4
1-3/4=1/4
So 12 book were 1/4 of the shipment.
So 48 book sis total.
If h = 7 find value of h2
Answers
If h = 7, then:
7(2)
= 14
Please I need help to doing this pleaseee help me
Answers
The equation of line in the given graph with coordinate points (2,-2) and (-3,-6) is 4x-5y=18.
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This value c is known as the y-axis intercept. Linear equations are classified into three types: point-slope, standard, and slope-intercept. The equation of a two-dimensional line is ax+by=c; it is fair to predict that the equation of a three-dimensional line is ax+by+cz=d; reasonable, but incorrect—it turns out that this is the equation of a plane. A plane, unlike a line, does not have a clear "direction."
Here,
The coordinates of line will be (2,-2) and (-3,-6).
slope m=(-6-(-2))/(-3-2)
=-4/-5
=4/5
(y-y1)=m(x-x1)
y+2=4/5(x-2)
5(y+2)=4(x-2)
5y+10=4x-8
4x-5y=18
4x-5y=18 is the equation of the line in the given graph with coordinate points (2,-2) and (-3,-6).
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What is the equation for the line that is perpendicular to y=−1/2x+5 and passes through the point (0, 7)?
Answers
The equation of line passes through the point (0, 7) will be;
⇒ y = 1/2x + 7
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (0, 7).
And, The perpendicular line is,
⇒ y = -1/2x + 5
Now,
Since, The equation of line passes through the point (0, 7).
So, We need to find the slope of the line.
Since, The product of slope of the perpendicular lines is - 1.
Hence, Slope of the perpendicular line is,
y = -1/2x + 5
m₁ = dy/dx = - 1/2
m₁ = - 1/2
So, The slope of the line,
m₂ = - (- 1/2)
= 1 / 2
Thus, The equation of line with slope 1/2 is,
⇒ y - 7 = 1/2 (x - 0)
⇒ y - 7 = 1/2 x
⇒ y = 1/2x + 7
Therefore, The equation of line passes through the point (0, 7) will be;
⇒ y = 1/2x + 7
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The lifeguards on a beach in Hawaii found a correlation between the height of a wave (y) and the number of surfers on the beach (x). The equation they calculated was y = 0.95x + 20. If the wave height was 4 feet, about how many surfers would be on the beach?
Answers
Answer:
Step-by-step explanation:
hope this helps
Please help with the following question.
Answers
Answer:
Step-by-step explanation:
C
Students in a cooking class made 4 1 2 quarts of soup. They served 4 5 of the soup to friends. Each serving is 3 5 quart. Hector incorrectly says that there were 3 3 5 servings of soup. What is the correct number of servings? What did Hector do wrong?
Answers
The correct number of servings would be = 12/25
What is a cooking class?A cooking class is defined as the class that is made up of students that are being thought how to prepare and serve different types of food.
The total amount of quarts of food made by the students = 4½.
The number of servings to friends = ⅘
The quantity of quarts in each serving = ⅗ quarts
Total number of quarts served = ⅘ × ⅗= 12/25
The correct number of servings = 12/25
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Which is equivalent to 644 ?
Answers
O 244
O 4
O 16
O 164/4
Michael is working two summer jobs, making $19 per hour lifeguarding and making
$14 per hour clearing tables. In a given week, he can work at most 17 total hours and
must earn a minimum of $280. If a represents the number of hours lifeguarding and
y represents the number of hours clearing tables, write and solve a system of
inequalities graphically and determine one possible solution.
Answers
The possible solutions are 8 hours and 9 hours.
The number of hours for lifeguarding is 8 hours.
The number of hours for clearing tables is 9 hours.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Two summer jobs:
Lifeguarding.
x = number of hours
= $19 per hour
Cleaning tables.
y = number of hours
=$14 per hour
Total hours in a week = 17 hours
Minimum earning = $280
The inequality represents the above situation.
x + y ≥ 17
19x + 14y ≥ 280
Solving for x and y.
x + y = 17 _____(1)
x = 17 - y
19x + 14y = 280 ______(2)
Putting (1) in (2) we get,
19(17 - y) + 14y = 280
323 - 19y + 14y = 280
323 - 5y = 280
323 - 280 = 5y
43 = 5y
y = 43/5
y = 8.6
y = 9
Now,
x = 17 - y
x = 17 - 8.6
x = 8.4
x = 8
Thus,
The possible solutions are 8 hours and 9 hours.
The number of hours for lifeguarding is 8 hours.
The number of hours for clearing tables is 9 hours.
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How many times did the team score less than 60 points?
Stem
4
5
6
7
Leaf
2,5,9
3,4,6,8,8,9
0,2,3,4,4,6,8
0,0,1,2
Answers
a certain species of bird migrates 10,000 miles in 75 days a person race walking can walk 20 kilometers in 100 minutes
who goes faster
Answers
A person race walking a distance of 20 kilometers in 100 minutes is more faster with a speed of 0.2 kilometer per minutes.
How to determine who is faster?Mathematically, the speed of a physical object or body can be calculated by using this formula;
Speed = distance/time
Next, we would convert the unit of distance covered by the bird in miles to kilometers as follows:
1 mile = 1.60934 kilometer.
10,000 miles = X kilometer.
Cross-multiplying, we have:
X kilometer = 10,000 miles × 1.60934 kilometer.
X kilometer = 16,093.4 kilometer.
Also, we would convert the unit of time in days to minutes as follows:
1 day = 1,440 minutes
75 days = X minutes
Cross-multiplying, we have:
X minutes = 75 days × 1,440
X minutes = 108,000 minutes.
Now, we can calculate the speed of this bird as follows:
Speed = 16,093.4/108,000
Speed = 0.1490 kilometer per minutes.
For the speed of the person, we have:
Speed = 20/100
Speed = 0.2 kilometer per minutes.
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During the time Tommy eat two bowls of ice cream, Robert eats three bowls of ice cream. The two boys ten bowls of ice cream in one hour. How many bowls did Tommy eat? Show working
Answers
Answer:20
Step-by-step explanation:
please help!! i do not understand
Answers
Answer:
Step-by-step explanation:
Hi, Julia, they are trying to ask about error, or the confidence that there is not an error. It's kinda like saying, we're 100% sure the answer is correct, mostly :DDDD which really lowers your confidence about the 100% correct statement. Anyway, sooo then they give the way to show deviation, from something. if you've had Calculus one, this is the same thing as the Delta , Epsilon thing, about a small distance away from the target is still with in a certain range. I feel like if they had written the inequality like this...
( p' - E) < p < (p'+E) it would be clearer about the inequality. E is just a tiny distance away in the positive and negative direction. E plays the role of epsilon. the numbers they give are the range of the confidence. I don't think they ask a very clear question.
0.056<p<0.112
p is kinda like our "best guess" answer, and we're giving it this range that it's probably within, for a certain level of confidence. You can see, that as the confidence goes down, that range can become bigger.
Which of the given formulas for the general term of the sequence 8, 5, 2, –1, –4, ...
is correct?
a. tn = −3n + 11
b. tn = 3n + 11
c. tn = 3n + 8
d. tn = 3n − 8
Answers
The term is tn=-3n+11
From the question, we have
The sequence is 8, 5, 2, –1, –4, ...
d = 5-8 = -3
t1 = 8
tn = t1+(n-1)d
tn=8+(n-1)(-3)
tn=8-3n+3
tn=-3n+11
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts,
Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting
Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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Write y=-|x-3|+2 as a piecewise function.
Answers
The equation y = -|x - 3| + 2 written as a piecewise function is;
f(x) = {y = x - 1, if x < -3
{y = -x + 1, if x ≥ -3
How to define piecewise functions?A function can be written as piecewise function if it changes its behavior ( increasing or decreasing ) about a point.
The function f(x) = y = |x| changes its behavior at |x| = 0 i.e , x = 0 .
y = | x | = x , if x < 0
= - x , if x > 0
| x | = a => x = ± a
• | x | ≥ a ( a ≥ 0 ) => x € ( -∞ , -a ] U [ a , ∞ )
• | x | ≤ a ( a ≥ 0 ) => x € [ -a , a ]
The given function is : y = -|x - 3| + 2
The function will change its behavior when; -| x - 3 | = 0
-x + 3 = 0
x = -3
If x < -3 , then ;
y = -(-(x - 3)) + 2
y = x -3 + 2
y = x - 1
If x ≥ -3, then ;
y = -(x - 3) + 2
y = -x + 3 + 2
y = -x + 1
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The length of the rectangular lot is 25 ft longer than twice the width. If the perimeter of the lot cannot exceed 350 ft, what is the greatest width possible?
Answers
The greatest width possible if the length of the rectangular lot is 25 ft longer than twice the width and if the perimeter of the lot cannot exceed 350 ft is 50 ft.
We are given,
The length of the rectangular lot is 25 ft longer than twice the width.
The perimeter of the lot cannot exceed 350 ft.
Let the width of the rectangular lot be x.
So, the length of the rectangular lot = 2x + 25
We know that the perimeter of the rectangle is given by:
P = 2(L + W)
Substitute the given values in the above formula;
350 = 2(2x +25 + x)
350 / 2 = 3x + 25
175 - 25 = 3x
x = 150 / 3
x = 50 ft
So, the width of the rectangular lot = 50 ft
And, the length of the rectangular lot = 2 * 50 + 25 = 125
Thus, the greatest width possible if the length of the rectangular lot is 25 ft longer than twice the width and if the perimeter of the lot cannot exceed 350 ft is 50 ft.
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3. Cameron has been given 4 boxes with samples
of soil. If all of the samples can either be
classified as mineral-rich, mineral-neutral, or
mineral-poor, how many different ways could
Cameron possibly classify all 4 samples, given
that they could all be classified as the same type
if that were the case?
A. 3
B. 4
C. 12
D. 81
Answers
Answer: D. 81
Step-by-step explanation:
Box A: 3 possibilites
Box B: 3 possibilites
And so on, so you get 3^4, which is 81
What are the domain and range of the function f(x) = 2x^3/4 respectively?
Answers
Answer:
Domain: [0,∞), {x|x ≥ 0}
Range: [0,∞), {y|y ≥ 0}
Step-by-step explanation:
1. Find where the FUNCTION is DEFINED.
A function is a set of ordered pairs where each first element is paired with one, and only one, second element. No element in either pair is without a partner.
2. Find the DOMAIN: The set of all x-values that a function passes through. Also, it is the left coordinate in a coordinate pair.
3. The RANGE: the set of all y-values that a function passes through. Also, it is the right coordinate in a coordinate pair.
A truck travels 50 m/s in a 30 second time frame what is the average speed
Answers
The average speed of the truck is 50 m/s .
We know that the average speed of any vehicle is calculated by total distance divide by total time.
Now the truck travels at 50 m/s for 30 seconds.
Distance covered in 30 seconds = 50 × 30 = 1500 meters
Time taken = 30 seconds
average speed = 1500 / 30 = 50 m/s
The average speed now accounts for the majority of the distance travelled. Average speed is essentially a method for calculating distance and the rate of transit time.
Knowing the average speed is crucial because it is clear that the pace will vary throughout the voyage. The average speed of a vehicle or an object can be determined using a variety of methods.
That is the most popular and simple way for figuring your average speed. It functions best when the object's speed remains constant throughout the journey, never rising or falling.
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Kye's current credit card balance is $3,109.87 with a minimum payment of $159.00. Over the next month he spends $532.42. If the APR is 27.99% (billed monthly), what will Kye's new balance be, with interest?
Answers
Therefore , the solution of the given problem of interest comes out to be $4,088.14 is the new balance.
What exactly does interest mean?Divide the number by the expense of borrowing, the remaining time, and other factors to get the simple interest rate. In marketing, the straightforward return plan is principal interest payments plus hours. This technique is the simplest way to figure out interest. The most common way to determine income is as a percentage of the principal sum.
Here,
We must first figure out the interest on the present balance.
The interest rate is 27.99%/12, or 0.0233, per month.
As a result, the current balance's interest rate is:
=> 3,109.87 x 0.0233 = $72.43
When this interest is added to the outstanding amount, Kye's new balance is as follows:
=> 3,109.87 + 72.43 + 532.42 = $3,714.72
The minimum payment for the new amount must now be determined:
=> 3,714.72 x 0.02 = $74.29
Kye's minimum payment for the following month will be $159.00 because the minimum payment is the higher of $74.29 or that amount.
Kye's new balance with interest as a result of making the required minimum contribution and spending $532.42 is as follows:
=> 3,714.72 - 159.00 + 532.42 = $4,088.14.
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Given: AB is parallel to CD and BD bisects AC.
Prove: triangle ABE is congruent to triangle CDE.
Answers
Check the picture below.
Explain what the vertical line test is and how it is used
Answers
Answer:
You take a pencil and slowly go across the graph from left to right. If any two points are under the pencil at any one time, the relations is not a function. For a relations to be a function, every input must have only one output, so there will be no two points graphed vertically on top of each other.
Step-by-step explanation:
How many different 10-letter words (real or imaginary) can be formed from the following letters? cbqgvlbbgc
Answers
Using mathematical permutation, there 30240 number of 10-letter words that can be formed from the arrangement of letters cbqgvlbbgc
What is permutation?Permutation is simply the manner of arrangement or selection of elements.
We shall calculate for the permutation of the letters cbqgvlbbgc as follows:
There are total of 10 letters
c = 2
b = 3
g = 2
q = 1
v = 1 and,
l = 1
permutation of cbqgvlbbgc = 10!/(2! × 2! × 3!)
permutation of cbqgvlbbgc = (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3!)/(2! × 2! × 3!)
dividing common factors of the numerator and denominator, we have
permutation of cbqgvlbbgc = 10 × 9 × 8 × 7 × 6 × 5
permutation of cbqgvlbbgc = 30240
Therefore by permutation, we derived 30240ways 10-letter words can be arranged from the letters cbqgvlbbgc.
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