Exponential Functions
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 multiplier (constant ratio)
What is the formula we use for exponential decay functions?
f(t) = a(1-r)t
Given the exponential function formula below:
f(x) = a * bx
Write the equation given a growth factor of 1/2 and an initial value of 100
f(x) = 100 * (1/2)x
What is the formula we use for exponential growth functions?
f(t) = a(1+r)t
How do you say red shoes in Spanish?
zapatos rojos
In the exponential function below:
f(x) = 2 * 3x, what is the initial amount/y-intercept?
a = 2
In the exponential growth formula,
f(t) = a(b)t, "b" is known as the _______.
growth factor
Given the exponential function formula below:
f(x) = a * bx
What does a represent?
the initial value
The number of people with the flu during an epidemic is a function, f, of the number of days, d, since the epidemic began. The equation f(d)=50*(3/2)^d defines f.
How many people had the flu at the beginning of the epidemic?
50 people
What is the human body's largest organ?
Skin
In the exponential function below:
f(x) = 4*(1/2)x, what is the growth factor?
b = 1/2
Solve:
f(t) = a(1 - r)t
a = 4500
r = 6%
t = 8 years
Round your answer to the nearest cent.
$2743.06
Given the exponential function formula below:
f(x) = a * bx
What happens to the graph if b > 1?
Solve:
f(t) = a(1 + r)t
a = 4500
r = 6%
t = 8 years
Round your answer to the nearest cent.
$7,172.32
In what sport can you win a Heisman trophy?
Football
The population of a city increases by 5% every year. If its population today is 300,000, what will its population be in 2 years?
330,750 people
A Rolls Royce with a star roof cost 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
Evaluate the function when x=1.5
f(x) = 3 * 4x
24
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
Which Hispanic country does the movie, Encanto, take place in?
Colombia
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
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 will the video stop being a fan favorite?
9 days
f(x) = 0.5x + 3
f(x)=0.5x
Compare these two graphs. What effect does the +3 seem to have on the graph?
Vertical translation 3 units up.
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
Name every person in the room :)
:)