Model each pair of situations with exponential functions f and g. Find the approximate value of x that makes f(x) = g(x).
25. F: initial value of 100 decreasing at a rate of 5%
G: initial value of 20 increasing at a rate of 5%
Answers
The model of the exponential functions
25:
f(x) = 100(0.95)ˣg(x) = 20(1.05)ˣf(x) = g(x) at x = -46.5326
f(x) = 40(1.25)ˣg(x) = 10,000(0.84)ˣf(x) = g(x) at x = 113.11How to model each pair of the functions with exponential functionConsidering the given problem, f(x) = a(b)^x
the starting = a
the base = b
the exponents = x
25.
F: initial value of 100 decreasing at a rate of 5%
a = 100, rate, r = 5%, b = 1 - 0.05 = 0.95
f(x) = 100(0.95)ˣ
G: initial value of 20 increasing at a rate of 5%
a = 20, rate, r = 5%, b = 1 + 0.05 = 1.05
g(x) = 20(1.05)ˣ
solving for f(x) = g(x)
20(1.05)ˣ = 100(0.92)ˣ
divide through by 20
(1.05)ˣ = 5(0.92)ˣ
x㏒(1.05) = ㏒(5 + (0.92)ˣ)
x㏒(1.05) = ㏒5 - x㏒0.92
x㏒(1.05) + x㏒0.92 = ㏒5
-0.015x = ㏒5
x = -46.53
26.
f: initial value of 40 increasing at a rate of 25%
a = 40, r = 25%, b = 1 + 0.25 = 1.25
f(x) = 40(1.25)ˣ
g: initial value of 10,000 decreasing at a rate of 16%
a = 10,000, r = 16%, b = 1 - 0.16 = 0.84
g(x) = 10,000(0.84)ˣ
solving for f(x) = g(x)
40(1.25)ˣ = 10,000(0.84)ˣ
divide through by 40
(1.25)ˣ = 250(0.84)ˣ
x㏒(1.25) = ㏒(250 + (0.84)ˣ)
x㏒(1.25) = ㏒250 - x㏒0.84
x㏒(1.25) + x㏒0.84 = ㏒250
0.0212x = ㏒250
x = 113.11
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Related Questions
Can someone help, please
Answers
Answer: 2 1/2 as a fraction
Hope this helps!
Answer:
9
Step-by-step explanation:
Write an exponential growth function to model each situation,
15. Initial value: 20
Growth factor: 1.25
Answers
Answer: f(x)=20(1.0125)^t
Step-by-step explanation:
use the formula P(1+r)^t when considering exponential growth (make it 1-r if decay)
P - principal (initial) value
r - growth rate (as a decimal! so divide by 100)
t - time (can be years, months, days, etc)
so now that we know the formula, just plug in everything you know!
P=20, r=0.0125, t=x
so the function is
20(1+0.0125)^t or 20(1.0125)^t
since we dont have a defined time, that becomes the variable for x, the one we can manipulate, so if they ask for 10 years, just replace t with 10!
A teapot can hold 45 liters of water what percentage of the pot is filled when it contains 9 liters of water?
Answers
Answer:
20%
Step-by-step explanation:
9/45 x 100
Answer:
20% of the pot is filled when it contains 9 litres of water.
Step-by-step explanation:
45 litres (total)
9 litres (filled)
9 ÷ 45 = 0.2
0.2 × 100 = 20
(Basically: [tex]\frac{9*100}{45}[/tex])
Which of the following questions describes the equation a/4 = -20?
A What number, when multiplied by four, is equal to negative twenty?
B What number, when divided by four, is equal to negative twenty?
C What number, when multiplied by negative twenty, is equal to four?
D What number, when divided by negative four, is equal to twenty?
Answers
Answer:
Option - What number , when divided by four , is equal to negative twenty is correct
Step-by-step explanation:
Given equation is
Rewrittting the given equation as below :
The number a is divided by 4 is equal to -20
Option question describes the given equation What number , when divided by four , is equal to negative twenty is correct
need help on this one
Answers
Answer:
Repeating
Repeating
Non-Repeating
repeating
Step-by-step explanation:
2. Repeating
3. Non-repeating
4. Repeating
Latanya plans to repaint some classroom
bookcases. She has 5 gallons of paint. All
of the bookcases are the same size and
each requires gallon of paint. What is
the maximum number of complete
bookcases she can paint?
Answers
This is the maximum number of complete bookcases she can paint.
Can someone help, please
Answers
Answer: the slope is -5/8
Step-by-step explanation: use desmos graphing calculator, it helps a lot. just put the 2 coordinates in and you see that the y value drops from 9 to 4, and the x value moves right from 1 to 9, hence -5/8
4x - 2(x - 2) = -9 + 5x - 8
Answers
Step by step
4x -2(x - 2) = -9 +5x -8
Distribute
4x -2x +4 = -9 +5x -8
Combine
2x + 4 = 5x -17
Subtract 5x from both sides to isolate variable
2x -5x +4 = 5x -5x -17
Combine
-3x +4 = -17
Subtract 4 from both sides to combine constants
-3x +4 -4 = -17 -4
Combine
-3x = -21
Divide both sides by -3 to solve
-3/-3 x = -21/-3
x = 7
PLEASE HELP AND GRAPH I WILL GIVE BRAINLIEST!!!!! IMAGES ADDED
Answers
What are the coordinates of point D(4/7, 3 1/3) after it reflected across the x-axis
Answers
Answer:it’s 4 units to the left
Step-by-step explanation: The point (4,3) reflected the x-axis,
=> The x remains the same, the y flips over the x-axis to be negative
(4,3) ==>> (4,-3)
The point (-3,-8) is reflected in the y-axis.
=> The y remains the same, the x flips over the y axis to be negative
(-3,-8)==>>(3,-8)
The point (2,4) is reflected in the line x = -3.
=> The x remains the same, the y flips over the x= -3 line.
Instead of reflecting over the x-axis (or the x = 0) line
and just being +4 or 4 above the x-axis to -4 or 4 below the x-axis-axis-axis
you have +4 being 7 above the x= -3 line so you need
7 below the x= -3 line or -10 SO
(2,4)==>>(2,-10)
The point (a, b) is reflected in the line y = x
Consider that the line x=y is a 45-degree diagonal.
Imagine a point on the 45-degree at +3 i.e. (3,0)
Imagine a line perpendicular to x=y from the point (3,0)
(sorry there is no way to draw on here - try drawing it)
The line would hit the x-axis-axis at (0,3)
So you can see the x becomes y and y become x.
(a,b)==>>(b,a)
For
ΔXYZ is defined by its vertices X(1,3), Y(-3,5), and Z(0, -5).
ΔXYZ is reflected in the y-axis.
So for each of the 3 points X, Y, and Z reflect about
the y-axis the same way in the second example above
and you will have the 3 new points X’, Y', and Z’
The translation T: (x, y) → (x -2, y + 4) maps the point (2, -3) to
The translation T: (x, y) → (x + 3, y - 2) maps the point (-4, -3) to
What you need to do here is just plug the values for X and Y into the translation.
e.g. for T: (x, y) → (x -2, y + 4) plug (2,-3) of x=2 y=-3 into (x -2, y + 4) and get the new values.
Solve -5w = -80 for w.
w=
Answers
Answer:
[tex]\huge\boxed{\sf w = 16}[/tex]
Step-by-step explanation:
Given equation:-5w = -80
Divide -5 to both sides
w = -80/-5
w = 16
[tex]\rule[225]{225}{2}[/tex]
—— ——
-5 -5
w=16
suppose the farmer buys 1/2 square mile of land and divides all his land into square fields 1/4 mile long and 1/4 mile wide how many fields will he have? What is the total area of his land in square miles?
Answers
Answer:
Step-by-step explanation:
Question 10 math homework
Answers
Answer:d
Step-by-step explanation:
ILL GIVE BRAINLISET
Simplify fraction with 7 minus 2 times 8 in the numerator and the cube root of 8 plus 6 in the denominator.
negative nine eighths
three eighths
negative three eighths
nine eighths
Answers
Simplified form of the fraction is -9/8. Therefore, option A is the correct answer.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Given that, (7-2×8)/(∛8+6).
= (7-16)/(2+6)
= -9/8
Therefore, option A is the correct answer.
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Days People
1 26
2 30
3 34
4 38
5 42
6 46
The chart shows how many people have signed up to go on a field trip each day. How many people would you expect to sign up on day 7?
Responses
A 4949
B 5050
C 4747
D 48
Answers
Each day the number of people goes up by four people, 46 + 4 = 50
Therefore there would be 50 people by day 7.
Explanation:
If you look at the number of people, you can see by how many days go by the number of people go up by +4. So, by the seventh day there should be 50 people because 46 + 4 = 50
Please help asap and explain how you did it! Tysm!!♡♡
Answers
Answer:
5
Step-by-step explanation:
The points have a distance of 5 away from eachother
Explanations:
1. Corey’s pay increases from £12.36 per hour to £14.11 per hour. Find the percentage increase to 1 decimal place.
Answers
Answer:
14.2% increase
Step-by-step explanation:
Corey’s pay increases from £12.36 per hour to £14.11 per hour. Find the percentage increase to 1 decimal place.
(14.11 - 12.36)/12.36 = 0.141586
0.141586 as a percent:
0.141586 * 100 = 14.2% increase
would be the answer
Can Someone Help Me Please?
Answers
Answer: 3x or 1 4/2x
Step-by-step explanation:
3/2x+1/2x+x=1 4/2x=3x
what is the of this expression 5/6 (1/8 / 3/4)
Answers
Answer:
2/3
Step-by-step explanation:
5/6-(1/8 / 3/4)
Skip flip multiply
5/6-(1/8x4/3)
5/6-(4/24)
5/6-(1/6)
4/6
2/3
hopes this helps please mark brainliest
help fast
expressions equivalent to 0.2(1.3x - 4.2) - x + 6.2
Answers
-0.74x + 5.36
Carrie is creating a painting for art class. The width of the canvas is 5 inches greater than the height of the canvas. Write a simplified equation in terms of h (the height) for the perimeter, p, of the canvas. (Please show works!!!)
Answers
Answer:
5h
Step-by-step explanation:
there isnt any out numbers so the answer is just 5h.
Since there are 4 sides, there are 4 terms.
Help. I'll mark as brainlist.
Answers
Answer:
Step-by-step explanation:
Angle ACD and Angle DCA you will realize that they represent the same angle.
The angle is the same,but just has two different names
Sandra earns $164 for working 16 hours and $512.50 for working 50 hours. The relationship between her income and the number of hours is proportional linear relationship. Determine the rate of Sandra's earnings.
Answers
she earns $10.25 an hour
Answer: 41/4
Step-by-step explanation:
1. Calculate 164/16
2. Simplify 41/4
3. Alternative Forms 10.25 or 10 1/4
1.John’s age is 12 more than 2 times Sam’s age. The sum of their ages is 65. How old are John and Sam?
2.The difference between two numbers is 28. Find the two numbers if the larger number is 3 times the smaller number.
3.Mary and Jim collect baseball cards. Mary has five more than three times as many cards as Jim. The total number of cards they both have is 147. How many cards do they each have?
Give brainliest
Answers
Answer:
2. 14 and 42
i hope it's right :)
Step-by-step explanation:
Let the number be x
So, the larger number = 3x
So the # is 14
Other #
42
The ages of John and Sam are 47.34 and 17.66 years respectively.
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.
Given, John’s age is 12 more than 2 times Sam’s age. The sum of their ages is 65.
Let, The age of Sam be 'x'.
Therefore, 2x + 12 + x = 65.
3x = 53.
x = 17.66.
So, Sam is 17.66 years old and john is (65 - 17.66) = 47.34 years old.
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Carl says the solution to a system of linear equations is (2, 6). What does Carl’s solution mean?
A. (2, 6) is the point of intersection for the lines of the two linear equations on a graph.
B. (2, 6) does not fall on the line for either equation.
C. The solution to one equation is x = 2 and the solution to the other equation is x = 6.
D. The point (2, 6) is the point of origin for one of the two equations.
Answers
HELP PLEASE!!
This table represents the number of ounces, u, a kitten grows after w, weeks.
When graphed, all of the points in the table lie on the same line.
What is the slope and y-intercept of the line?
slope=2/3, y-intercept=−0.2
slope=−3/2, y-intercept = 3
slope= 3/2, y-intercept = 3
slope= −2/3, y-intercept=−0.2
Answers
Y intercept is the value of y at x = 0
At x = 0, y = 3
Y intercept is 3
The rate of growth of the cat is positive, meaning thats it gains, not loses, weight.
Option C is the only correct one.
It has a positive slope, and a y intercept of 3
To solve for slope mathematically, pick two points.
(0, 3) (6,12)
(x1, y1) (x2, y2)
or
(x2, y2) (x1, y1)
Pick which one is x1 and y1 and x2 and y2 based on what seems easier to calculate
Slope is equal to [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{12-3}{6-0}[/tex]
9/6
slope is 3/2
Hope this helps,
Jeron
:)
need help again please
Answers
Answer:
Part A:
8 x 7 = 56; 56 x 10 = 560
Part B:
504
Part A & B explanation:
If you notice, there are no decimals in the answers so it's clear they round them. 8.4 rounded is 8 & 6.9 rounded is 7. To find the area of a singular rectangle is length x width. 8 x 7 = 56. In part A the directions say "best estimate" signaling that it isn't the exact answer you're looking for. 8 x 7 = 56; 56 x 9 = 504 would be the exact answer. (Answer for part b).Therefore, the answer for part A is 8 x 7 = 56; 56 x 10 = 560. Because 560 is the closest to 504 on the board.
Hope this helped <3
One boxcar of a model train measures 6 inches in length. The actual length of a boxcar is 606 inches (50.5 ft). What is the scale of the model?
Answers
Answer:
56.ft
Step-by-step explanation:
Answer:
56 feet
Step-by-step explanation:
Hari gives Sai some money. If 1/9 of the money was spent on food and 2/5 of the money was spent on clothes, how much money did Hari give to Sai?
Answers
220.
Explanation:
1/9 -> 450=50
2/5 -> 450=180
180+50=230
450-230=220.
Help pls, v2 of last question. Zoom in if needed
Answers
Answer: I'm not 100% sure what you're asking for, but the full answer to the last question is a .25 increase or a 25% increase.
Step-by-step explanation:
First, we need to see how much it increases.
We would take 1.50, and minus 1.25 from it to get our first answer of .25.
To get the percentage of increase, we would take our .25, and times it by 100 equaling 25%.