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The $1,000 invested in a simple savings account earns 6% interest each year.

a) Write an equation.

b) How much money will be in account after 10 years?

a) Write an equation.

b) How much money will be in account after 10 years?

a) y = 1,000 (1.06)ⁿ

b) $1,790.85

b) $1,790.85

Janelle invests $2,000 in a savings account, which earns 5% interest per year.

a) Write an equation.

b) Approximately how many years will it take for the original amount to double in value?

a) Write an equation.

b) Approximately how many years will it take for the original amount to double in value?

a) y = 2,000 (1.05)ⁿ

b) 15 years ≈$4,157.86

b) 15 years ≈$4,157.86

The population of Tribetts (insect) decreases by 30% each year. The starting population was 10,000.

a) Write an equation.

b) Make a table showing the number of Tribetts (insect) at the end of the first five years.

c) In what year will there first be fewer than 1,000 Tribetts (insect).

a) Write an equation.

b) Make a table showing the number of Tribetts (insect) at the end of the first five years.

c) In what year will there first be fewer than 1,000 Tribetts (insect).

a) y = 10,000 (.70)ⁿ

b) Years-------Tribetts

0 ----------10,000

1----------- 7,000

2------------ 4,900

3------------- 3,430

4-------------2,401

5-------------1,681

c) 7 years ≈824

b) Years-------Tribetts

0 ----------10,000

1----------- 7,000

2------------ 4,900

3------------- 3,430

4-------------2,401

5-------------1,681

c) 7 years ≈824

Write an exponential equation, find the amount after the specified time.

Suppose the acreage (quantity of acres) of forest is decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, determine the amount of forest land after 6 years.

Suppose the acreage (quantity of acres) of forest is decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, determine the amount of forest land after 6 years.

4,500,000 (.98)⁶ = $3,986,290

Write an exponential equation, find the amount after the specified time.

A $10,500 investment has a 15% loss each year. Determine the value of the investment after 4 years.

A $10,500 investment has a 15% loss each year. Determine the value of the investment after 4 years.

10,500 (.85)⁴ = $5981.07

y = 40,000 (1.34)ⁿ

What is the initial amount, growth factor, growth rate (% increase)?

What is the initial amount, growth factor, growth rate (% increase)?

Initial amount = 40,000

Growth Factor = 1.34

Growth Rate = 34%

Growth Factor = 1.34

Growth Rate = 34%

y = 19 (.86)ⁿ

What is the initial amount, decay factor, decay rate?

What is the initial amount, decay factor, decay rate?

Initial amount = 19

Decay Factor = .86

Decay Rate = 14%

Decay Factor = .86

Decay Rate = 14%

Does the equation model growth or decay?

y = 300 (1.7)ⁿ

y = 300 (1.7)ⁿ

Growth, because exponential factor is greater than 1.

Does the equation model growth or decay?

y = 9 (1.02)ⁿ

y = 9 (1.02)ⁿ

Growth, because exponential factor is greater than 1.

Does the equation model growth or decay?

y = 657 (.8)ⁿ

y = 657 (.8)ⁿ

Decay, because exponential factor is less than 1.

Does the equation model growth or decay?

y = 56 (.04)ⁿ

y = 56 (.04)ⁿ

Decay, because exponential factor is less than 1.