Exponential Growth & Decay

Exponential Rules

100

Simplify the following: (give your answer as one number without an exponent) 8⁹/8⁷

What is 64

200

Simplify the following: (5a³)³

125a⁹

300

Simplify the following: 5a^-2b⁷

What is 5b⁷/a²

400

Simplify: (3a³b²)³

27a⁹b⁶

500

Simplify: (-2a^-3b⁶)^-3

a⁹/(-8b¹⁸)

Word Problems

100

The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the number of years it takes for the population to grow to 42,500.

What is approximately 9 years

200

$1,200 is invested at an annual rate of 3.2%. Find the number of years it will take for the account balance to be $1,480.

What is approximately 6.7 years

300

The population in the town of Deersburgh is presently 42,500. The town has been growing at a steady rate of 2.7%. Find the number of years ago that the population was 30,000.

What is approximately 13 years

400

The value of a stock when purchased was $10 a share. The stock grew at a monthly rate of 7%. Find the number of months it took to reach a value of $15.75 a share.

What is approximately 6.7 months

500

The value of a stock when purchased is $10 a share. The stock decreased at a rate of 3% daily. Find the number of days it took for the stock to be worth $7.40.

What is almost 10 days (approximately 9.9 days)

Growth Rate/Factor

100

Use y = 250(1.2)^t What is the y-intercept?

What is 250

200

Use y = 250(1.2)^t What is the growth factor?

What is 1.2

300

Use y = 250(1.2)^t What is the growth rate?

What is 20%

400

y = 9.8(1.35)^t What is the growth factor?

What is 1.35

500

y = 9.8(1.35)^t What is the growth rate?

What is 35%

Write the Equation

100

Write an exponential growth function to model the situation. A population of 422,000 increases by 12% each year.

What is y= 422,000(1.12)^t

200

The population of Baconburg starts off at 20,000, and grows by 13% each year. Write an exponential growth model and find the population after 10 years.

What is y = 20,000(1.13)¹⁰ and population of 67,891

300

The Hippityhoppity bunny decided to have a family reunion at the Magic Forest every 5 years. During the second reunion the family discovered that the number of family members was 154 and was growing at an annual rate of 3.2%. Write an equation to model the growth of the bunny family.

What is y = 154(1.032)^x

400

The fish in The Magic Forest Lake were declining at an annual rate at 1.5%. Their current number is estimated at 2500. Write an equation to model the decreasing number of fish.

What is y = 2500(.985)^x

500

The fish in The Magic Forest Lake were declining at an annual rate at 1.5%. Their current number is estimated at 2500. Write an equation to predict the number of fish in the lake in 10 years.

What is y = 2500(.985)¹⁰

T-Charts

100

What is the growth factor for the following t-chart? 

y/ 1 / 3 / 9 / 12 / 81 / 

x/ 0 / 1 / 2 / 3 / 4 /

What is 3

200

What is the y-intercept for the following t-chart? 

y/ 1 / 3 / 9 / 12 / 81 / 

x/ 0 / 1 / 2 / 3 / 4 /

What is 1

300

What is the y-intercept for the following t-chart? 

y/ 12 / 36 / 108 / 324 / 972 / 

x/ 1 / 2 / 3 / 4 / 5 /

What is 4

400

What is the growth factor for the following t-chart? 

y/ 4 / 9.6 / 23.04 / 55.29 / 132.7 / 

x/ 0 / 1 / 2 / 3 / 4 /

What is 2.4

500

What is the growth factor and the y-intercept for the following t-chart? (must get both correct) 

y/ 31.2 / 121.7 / 474.6 / 1850.8 / 7217.9 / 

x/ 1 / 2 / 3 / 4 / 5 /

Growth Factor: 3.9 Y-intercept: 8