Exponential Growth and Decay

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent 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 consistent percentage over a period of time, leading to rapid decreases as the base amount 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

If a population of 1000 increases by 10% each year, what will it be after 3 years?

Back

A = 1000(1 + 0.10)^3 = 1331.

Front

If a substance has a half-life of 5 years, how much of a 100g sample remains after 15 years?

Back

After 15 years, 12.5g remains (100g -> 50g -> 25g -> 12.5g).

Front

What does the term 'doubling time' refer to in exponential growth?

Back

Doubling time is the period it takes for a quantity to double in size at a constant growth rate.

Front

How do you identify an exponential growth model from an equation?

Back

An exponential growth model has a base greater than 1, e.g., A = P(1 + r)^t.

Front

How do you identify an exponential decay model from an equation?

Back

An exponential decay model has a base less than 1, e.g., A = P(1 - r)^t.

Front

What is the value of a home worth today if it was purchased for $160,000 and appreciates at 5% per year for 20 years?

Back

$424,527.63.