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 growth as time progresses.

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 time progresses.

Front

What is the formula for Exponential Growth?

Back

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

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

If a population of 1000 increases by 20% each year, what will it be after 3 years?

Back

A = 1000(1 + 0.20)^3 = 1,728.

Front

If a substance decays from 500 grams to 250 grams in 2 years, what is the decay factor?

Back

The decay factor is 0.5.

Front

What does a decay factor of 0.85 indicate?

Back

It indicates that the quantity decreases to 85% of its previous value each time period.

Front

How do you identify Exponential Growth on a graph?

Back

Exponential Growth is identified by a curve that rises steeply as it moves to the right.

Front

How do you identify Exponential Decay on a graph?

Back

Exponential Decay is identified by a curve that falls steeply as it moves to the right.

Front

What is a common ratio in exponential functions?

Back

The common ratio is the factor by which a quantity multiplies during each time period in exponential growth or decay.