Exponential Functions
Exponential Decay
Transformations of Exponential Functions
Exponential Growth
Trivia
100
Fill in the blanks: Exponential Functions are modeled using f(x) = a ∙ bx, where a is the ________ and b is the __________.
initial amount/y-intercept, constant ratio
100
What is the formula we use for exponential decay functions?
f(t) = a(1 - r)t
100
Given the exponential function formula below:
f(x) = a * bx + k
What does k represent?
A vertical translation
100
What is the formula we use for exponential growth functions?
f(t) = a(1 + r)t
100
What's their name?
Flower
200
In the exponential function below:
f(x) = 2 * 3x, what is the initial amount/y-intercept?
a = 2
200
In the exponential growth formula,
f(t) = a(1 - r)t, "1-r" is known as the _______.
Decay factor
200
Given the exponential function formula below:
f(x) = a * bx-h
What does h represent?
A horizontal translation
200
In the exponential growth formula,
f(t) = a(1 + r)t, "1+r" is known as the _______.
Growth factor
200
What is the most recent season of Survivor?
300
In the exponential function below:
f(x) = 4 * 1/2x, what is the constant ratio?
b = 1/2
300
Solve the problem:
f(t) = a(1 - r)t
a = 4500
r = 6%
t = 8 years
Round your answer to the nearest cent.
$2743.06
300
Given the exponential function formula below:
f(x) = a * bx
What happens to graph if a is > 1?
It gets narrower.
300
Solve the problem:
f(t) = a(1 + r)t
a = 4500
r = 6%
t = 8 years
Round your answer to the nearest cent.
$7,172.32
300
What is the diameter of golf ball?
1.68 inches
400
What is the written form of the exponential function represented by the given table:
x y
0 4
1 12
2 36
3 108
f(x) = 4 * 3x
400
A video is labeled a fan favorite if it receives at least 1,000 views per day. Amelia posts a video that gets 6,465 views on the first day. The number of views decreases by 20% each day after that. In how many days total will the video stop being a fan favorite?
9 days
400
f(x) = 0.5x + 3
Describe the transformation.
Vertical translation 3 units up.
400
The population of Hillville is 10,000 residents and grows at an annual rate of 20%. What will the estimated population of Hillville be in five years?
24,883 residents
400
How many properties are on the Monopoly board?
28
500
Graph the exponential function given below on a piece of paper. You cannot use desmos.
f(x) = 2(3)x
Ms. B will check :)
500
A Rolls Royce with a star roof costed Jimmy $450,000. The value of the vehicle depreciated by 12% every year. What would the value of the car be after 10 years?
Approximately $125,325
500
Describe the transformation given the function below:
f(x) = 3 * 4x-2 - 3
Horizontal translation 2 units to the right. Vertical translation 3 units down. Y-intercept/initial amount = 3.
500
The value of a pair of Fire Red 4 Jordan's increases by 10 percent every year. If the shoes were purchased 9 years ago for $140, how much is it worth today?
Approximately $330
500
By U.S. law, exit signs must be one of what two colors?
Red or green