Exponential Functions

Substitution

100

g(x) = 7 * 2^x

Calculate g(x) when x = 3

g(x) = 56

200

y = 4 * 2^x

Calculate y when x = 0.

y = 4

300

f(x) = 120(0.97)^x

Find f(x) when x = 3. 

f(x) = 109.52

Creating

100

Kylie owes her credit card company $100. Each month that her payment is late, her debt (the amount she owes) doubles.

What is the initial value (a) for the exponential function that models this scenario?

a = 100

200

Kylie owes her credit card company $100. Each month that her payment is late, her debt (the amount she owes) doubles.

What is the multiplier (b) for the exponential function that models this scenario?

b = 2

300

Kylie owes her credit card company $100. Each month that her payment is late, her debt (the amount she owes) doubles.

Write an equation to represent the amount Kylie owes based on the number of months late her payment occurs.

y = 100 * 2^x

Growth or Decay

100

Is the function below an example of exponential growth or exponential decay?

P(t) = 340(0.52)^t

Exponential Decay

200

Is the function below an example of exponential growth or exponential decay?

N(x) = 65(1.03)^x

Exponential Growth

300

Is the function below an example of exponential growth or exponential decay?

y = 0.62(1.17)^x

Exponential Growth

Interpreting I

100

The function f(x) = 840(1.03)^x represents the number of students who attend New High School x years after its opening in 2020.

What is the meaning of f(2) = 900?

The student population 2 years after its opening in 2020 is 900.

200

The function f(t) = 535(0.97)^t  represents the population of a specific fish species present in a small creek over t years since 1950.

What is the meaning of f(3) = 500?

The fish population 3 years after 1950 is 500.

300

Function S(t) = 80(1.2)^t represents the amount in Geraldine's bank account after t weeks of saving her money.

What is the meaning of S(10) = 300?

The amount in Geraldine's bank account after 10 weeks is $300.

Interpreting II

100

The function f(x) = 840(1.03)^x represents the number of students who attend New High School x years after its opening. 

How is the number of students changing over time? Provide a percent and if the student population is increasing or decreasing. 

3% increase per year

200

The function f(t) = 535(0.97)^t  represents the population of a specific fish species present in a small creek over t years.

How is the fish population changing over time? Provide a percent and if the population is increasing or decreasing. 

Decreasing by 3% each year.

300

Function S(t) = 80(1.2)^t represents the amount in Geraldine's bank account after t weeks of saving her money.

How is Geraldine's amount in her bank account changing over time? Provide a percent increase or decrease.

20% increase per week.