Exponential Growth/Decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, leading to a rapid increase in value.

Tags

CCSS.HSF-LE.A.1A

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 in value.

Tags

CCSS.HSF-IF.C.8B

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 11.2% becomes 0.112.

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

If a population of fish increases by 15% per year, what type of change is this?

Back

This is an example of exponential growth.

Tags

CCSS.HSF-LE.A.1A

Front

If a man loses 2% of his hair each year, what type of change is this?

Back

This is an example of exponential decay.

Tags

CCSS.HSF-LE.A.1A

Front

What happens to the value of an investment with a positive interest rate over time?

Back

The value of the investment will grow exponentially over time.

Tags

CCSS.HSF-LE.A.1C

Front

What happens to the value of an asset that depreciates by a fixed percentage each year?

Back

The value of the asset will decay exponentially over time.

Tags

CCSS.HSF-IF.C.8B

Front

If a house is worth $150,000 and appreciates at 2% per year, what will its value be after one year?

Back

The value after one year will be $150,000 * (1 + 0.02) = $153,000.

Tags

CCSS.HSF.BF.A.2