Growth or Decay?
Writing Exponential Functions
Applying Exponential Functions
Components of Exponential Equations
Miscellaneous
100
Is the following growth or decay: f(x) = 2x
Growth
100
Cyril's new Tesla truck was $50,000 when he first bought it. Its value decreased by 0.75 every year.
Write an exponential equation
y=50000(0.75)x
100
The equation f(x) = 422,000(1.12)x represents the population of a city every year. In 15 years, what will the population of the town be?
about 2,309,844 people
f(15) = 422,000(1.12)15
100
What is the constant multiplier in y = 4•2x?
2
100
This is the formula for exponential functions
What is y = a(b)x?
200
Is the following growth or decay: f(x)=100(0.5)x
Decay
200
Amara invests $1,200, which goes up at a rate of 1.2 every year.
Write an exponential equation.
f(x)=1,200(1.2)x
200
The following equation represents the amount of Elephants over the course of a number of years:
f(x) = 20,000(0.85)x
If they started taking the data in 2010, how many elephants will there be in 2020?
about 3,937 elephants
f(10) = 20,000(0.85)10
200
What is the y-intercept in y = 3x?
1 or (0, 1)
y = 1•3x
200
Write the exponential function that has a constant multiplier of 5 and y-intercept at (0, 0.2).
y = 0.2•5x
300
Is the following growth or decay?
Table by S Holmes using Google Drawings, free per terms of use
Decay
300
Mr. Miller decides he wants to grow a beard. His starts measuring when his beard is 2 cm long. Every week, it grows by 5%.
Write an exponential equation.
y=2(1.05)x
300
A bunny family totaled 154 in 2018. The family grew at an annual rate of 1.032. How large will the family be 2025?
about 192 bunnies
f(2025-2018) = 154(1.032)7
300
What is the constant multiplier in an exponential function that is decreasing 10% each year?
90% or 0.9
100% - 10% = 90%
300
These ordered pairs represent an exponential function; (-1, .5),(0,3),(1,18),(2,108). True or false, explain your answer.
False there is a constant multiplier (6).
400
Is the following growth or decay?
An electrical store calculates that the number of DVD players sold is decreasing by 13% per year.
Decay
400
Zion's only made 24 three pointers when he was in college. He's going to practice and improve his shots by 15% every year.
Write an exponential equation.
y=24(1.15)x
400
The fish in Lake Washington were declining at an annual rate at 1.5%. Their current number is estimated at 2500. How many fish will there be 20 years from now?
about 1,847 fish
f(20) = 2500(.985)20
400
Write a simplified exponential function for the scenario. An investment of $20,000 earns 2.5% interest each year.
y = 20,000•(1.025)x
100% + 2.5% = 102.5% = 1.025
400
What equation represents the graph below?
Graph by S Holmes using Graphfree.com, free per terms of use
y = 8(1/2)x
500
The population of an ant colony increases at a rate of 44% per week.
Growth
500
Lamar purchases some stock at the value of $20 a share. The next day, that stock was down to $8, and on the second day, it was worth $3.20.
Write an exponential equation.
y=20(0.4)x
500
Serena bought a laptop 4 years ago, but she doesn't remember how much it cost. But right now, she knows it's worth $1,024. She knows it decreases in value by 20%.
How much did she buy it for?
$2500
1,024=b(0.8)4
500
Write a simplified exponential function for the scenario. An investment of $650 depreciates by 1.1% per year.
y = 650•(0.989)x
100% - 1.1% = 98.9% = 0.989
500
Write the exponential function for the given values.
x: 0, 1, 2
y: 2560, 3200, 4000
y = 2560•1.25x