Exponential Functions

Identify that Rate

100

Is the following exponential function below exponential growth or decay? And why? f(x)=4(.75)^x

What is Exponential Decay Because (b)<1

200

Is the following exponential function below exponential growth or decay? And why? f(x)=4(7/5)^x

What is Exponential Growth Because (b)>1

300

Given y=2(1.65)^x, Identify if the function is growth or decay. Then Identify the Growth/Decay Rate.

What is Exponential Growth rate is .65 or 65%

400

Given y=2(3/5)^x, Identify if the function is growth or decay. Then Identify the Growth/Decay Rate.

What is 2/5 or .40 or 40%(Decay)

500

Given y=100(.47)^x, Identify if the function is growth or decay. Then Identify the Growth/Decay Rate.

What is .53 or 53% (Decay)

Write that function

100

Mason takes 400 mg of Advil for a headache. Every hour, the Advil dissolves 18%. Write a function that models the amount of Advil in Mason's body.

What is F(n)=400(1-.18)ⁿ

200

In 2000, there were 670 cell phone subscribers in the small town of Homer. The number of subscribers increases by 65% per year after the year 2000. Write a function to represent this model.

What is f(n)=670(1+.65)ⁿ

300

You invest $450 in a stock that increases in value at an annual rate of 15% per year. Write a function that models the value of the stock over 15 years.

What is f(15)=450(1+.15)¹⁵

400

Billy sold a football trading card for 306,000 in 2002.Since then, the value has increased by 2% each year. What will the card be worth next year(2018)? Write the function that represents this model.

What is f(16)=306,000(1+.02)¹⁶

500

Each year Hood College hosts a tennis tournament. The tournament starts with 128 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds? Write a function that represents this model.

What is f(5)= 128(1-.50)⁵

State that Shift

100

Using f(x)=200(1.5)^x  State the equation with a transformation of right 3 and down two.

What is f(x)=200(1.5)^{(x-3) -2}

200

Using f(x)=2(.75)^x State the equation with a transformation of right 7 and up 4 two.

What is f(x)=2(.75)^{(x-7) + 4}

300

Using f(x)=177(1.07)^xState the equation with a transformation of down 11.

What is f(x)=177(1.07)^{x -11}

400

Using f(x)=2(.75)^x State the equation with a transformation of left 3 and down one.

What is f(x)=3(.75)^{(x+3) -1}

500

Using f(x)=30(.5)^x State the equation with a transformation of right 7 and up twenty-two.

What is f(x)=30(.5)^{(x-7) + 22}

Vocab and Formulas

100

Growth Model Formula

What is a(1+r)ⁿ

200

Decay Model Function

What is a(1-r)ⁿ

300

The number represented by (1+r) or (1-r) in the exponential growth or decay formulas represents what?

What is Growth/Decay Factor

400

The "a" in the exponential growth and decay formulas represent what?

What is Initial/Starting amount

500

What is the initial amount (When x=0)called on a graph?

What is y intercept

Solve the Model

100

Your parents invest $1000 in a stock that increases 4% every year. How much will the stock be worth after 12 years?

What is $1601.03

200

FREE SPACE

What is If it's FREE, it's for MEEE!!!

300

The current population of the panda in Alaska is 2503. It is decreasing by 11% each year. What will be the population of pandas in 2022?

What is 1398

400

Sarah bought a tv in 1995 for $550. The value of the tv depreciated 7% each year. What was the cost of the tv in the year 2001?

What is $355.84

500

John bought a trading baseball card in 1980 for $280. The value of the card increases 3% each year. What will the price of the car be in 2030?

What is $1227.49