Growth or Decay?
Writing Exponential Functions
Applying Exponential Functions
Transforming Exponential Functions
Potpourri
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?
What is about 2,309,844
f(x) = 422,000(1.12)15
100
Describe the transformation in the following function:
f(x) = 2x
g(x) = 2x +5
Translated up 5 units
100
This is the formula for exponential functions
What is 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?
What is about 3,937
f(x) = 20,000(0.85)10
200
Describe the transformation in the following function:
f(x) = ex
g(x) = e(x+4)
Translated four units to the left
200
Suppose that $5000 is deposited in a saving account at the rate of 6% per year. It's compounded quarterly. Find the total amount on deposit at the end of 4 years.
$6344.93
A= 5000(1.015)16
300
Is the following growth or decay?
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?
What is about 192
f(x) = 154(1.032)7
300
Describe the transformation in the following function:
f(x) = 0.5x
g(x)= 0.5-x
Reflected over the y axis
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?
What is about 1,847 fish
y = 2500(.985)20
400
Describe the transformations that took place:
BONUS: Can you write the equation?
Blue = 3x
Reflected over the x-axis, translated down 4 units
y= -3x-4
400
Ryan invests $2000 in a savings account with a fixed annual interest rate of 10% compounded 8 times per year. What is his balance after 10 years?
$5,402.97
2000(1.0125)80
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 wroth $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?
What is $2500
1,024=b(0.8)4
500
Describe the transformations that took place:
BONUS: Can you write the equation?
Blue = ex
Reflected over the x-axis, moved up 4, and dilated by 2
-2ex+4
500
The population of a town is declining at a rate of 6%. If the current population is 12,426 , predict the population in 10 years using a continuously.
6820 people