5.3 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 time progresses.

Tags

CCSS.HSF-LE.A.1A

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 time progresses.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate the decay factor?

Back

The decay factor is calculated as 1 - r, where r is the decay rate expressed as a decimal.

Tags

CCSS.HSF-IF.C.8B

Front

If a population doubles every 3 months, what is the growth factor?

Back

The growth factor is 2, as the population doubles.

Tags

CCSS.HSF-LE.A.1C

Front

What is a common example of exponential decay in real life?

Back

A common example is the depreciation of a car's value over time.

Front

What does a growth rate of 25% mean?

Back

It means that the quantity increases by 25% of its current value each period.

Tags

CCSS.HSF-IF.C.8B

Front

What does a decay rate of 8% mean?

Back

It means that the quantity decreases by 8% of its current value each year.

Tags

CCSS.HSF-IF.C.8B

Front

How do you model exponential growth?

Back

You can model exponential growth using the formula A = P(1 + r)^t, substituting the values for P, r, and t.

Tags

CCSS.HSF-LE.A.1A