HW - 6.5 Exponential Growth & Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, leading to rapid increases as the quantity grows.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease as the quantity shrinks.

Front

What is the formula for exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula is A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

How do you calculate the value of an investment after a certain number of years with exponential decay?

Back

Use the formula A = P(1 - r)^t, substituting P for the initial investment, r for the decay rate, and t for the number of years.

Front

How do you calculate the future population with exponential growth?

Back

Use the formula A = P(1 + r)^t, where P is the current population, r is the growth rate, and t is the number of years.

Front

If an investment of $8200 loses value at a rate of 2% per year, what is its value after 9 years?

Back

The value after 9 years is approximately $6836.73.

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If a town's population is 1600 and increases at a rate of 3% per year, what will it be after 10 years?

Back

The population after 10 years will be approximately 2150.

Front

What is the expected annual sales after 7 years if current sales are $149,999 and increase at 6% per year?

Back

The expected annual sales after 7 years will be approximately $225,543.04.

Front

If a town's population decreases at a rate of 1% per year from 1300 in 2000, what will it be in 2008?

Back

The population in 2008 will be approximately 1199.