Exponential Growth and 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 base amount 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 rapid decreases as the base amount shrinks.

Front

Define the growth rate (r) in an exponential function.

Back

The growth rate (r) is the percentage increase per time period in an exponential function, often expressed as a decimal.

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 future value of an investment with exponential growth?

Back

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

Front

How do you calculate the future value of an asset with exponential decay?

Back

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

Front

What does a decay rate of 15% mean in an exponential decay model?

Back

It means that each year, the value decreases by 15% of its value from the previous year.

Front

If a quantity decreases by 5% each year, what is the decay factor?

Back

The decay factor is 0.95, calculated as 1 - 0.05.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.