Exponential Functions

Exponential Growth

100

Suppose 25 wolves are released in northern Michigan, and the yearly growth factor for this population is expected to be 1.7. Write a NOW-NEXT rule that models the growth of the wolf population.

Start: 25  Next=Now * 1.7

200

Suppose 20 wolves are released in northern Michigan, and the yearly growth factor for this population is expected to be 1.5. Write an explicit function (y = …) that can be used to model the growth of the wolf population.

y=20(1.5^x)

300

Write an explicit function (y = …) for table provided. 

y=3(2^x)

400

Suppose 25 wolves are released in northern Michigan, and the yearly growth factor for this population is expected to be 1.5. How long will it take for the new wolf population to exceed 150?

5 years

500

Suppose 15 wolves are released in northern Michigan, and the yearly growth factor for this population is expected to be 1.7. What is the % growth from one year to the next?

70 %

Exponential Decay

100

If an amount of Strontium-90 is stored at the beginning of a year, 85% of that amount will still be present at the end of the year. Write a Now-Next rule that shows how to calculate the amount of Strontium-90 remaining from an initial amount of 100 grams at any year in the future. 

Start: 100 Next=Now * .85

200

One hour after ingestion, 75% of the original amount of caffeine in coffee remains. Suppose a person consumes 45 milligrams of caffeine. Write an explicit function (y = …) that can be used to calculate the amount of caffeine that will remain x hours after the initial dose.

y=45(.75^x)  

300

If an amount of Strontium-90 is stored at the beginning of a year, 95% of that amount will still be present at the end of the year. If 100 grams are released by accident, how much of that radioactive substance will still be around after 3 years?

85.7 grams

400

One hour after ingestion, 75% of the original amount of caffeine in coffee remains. Suppose a person consumes 50 milligrams of caffeine. Estimate to the nearest tenth the number of hours it will take for 5 milligrams of caffeine to remain. 

8 hours

500

If an amount of Strontium-90 is stored at the beginning of a year, 92% of that amount will still be present at the end of the year. If 100 grams are released by accident, estimate to the nearest tenth, the half-life of Strontium-90.

8.3 years

Properties of Exponents

100

Simplify the Value

6⁵/6³

36

200

Simplify the Value

(3xy²)(xy)⁴

3x⁵y⁶

300

Simplify the Value

x³/x^-5

x⁸

400

Simplify the Value

(5⁵5^-24^-2)/(5⁴4^-27⁰)

.2

500

Simplify the Value

((3a³b³c⁰)/(3a³b⁴c³))^-4

b⁴c¹²

Exponential Translations

100

Describe the Translation

f(x)=3^x+6

up 6 units

200

Describe the Translation

f(x)=3^x-2

right 2 units

300

Describe the Translation

f(x)=3^x+5

left 5 units

400

Describe the Translation

f(x)=3^x-2+8

right 2 units, up 8 units

500

Describe the Translation

f(x)=3^x+4-5

left 4 units, down 5 units

Random

100

On a standard traffic light, is the green on the top or bottom?

Bottom

200

How many curves are in a standard paper clip?

3

300

On the back of a dollar bill, what is in the center?

ONE

400

How many Battle Stars do you need to reach max tier in Season Three of Fortnite?

1000

500

What is Harry Potter's middle name? 

James