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, resulting in 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 consistent percentage over a period of time, leading to a rapid decrease in value.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a(b)^x, where 'a' is the initial amount, 'b' is the growth (b > 1) or decay factor (0 < b < 1), and 'x' is the time.

Tags

CCSS.HSF.LE.A.2

Front

What does the term 'initial amount' refer to in an exponential function?

Back

The initial amount is the value of the function when x = 0, represented by 'a' in the function f(x) = a(b)^x.

Tags

CCSS.HSF.LE.B.5

Front

How do you determine the growth factor from an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b)^x, where b > 1 indicates growth.

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine the decay factor from an exponential function?

Back

The decay factor is the base 'b' in the function f(x) = a(b)^x, where 0 < b < 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula to calculate the decay factor from a percentage rate?

Back

The decay factor can be calculated using the formula (1 - r), where r is the rate of decay expressed as a decimal.

Tags

CCSS.HSF-IF.C.8B

Front

If a quantity decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.80, calculated as (1 - 0.20).

Tags

CCSS.HSF-LE.A.1C

Front

What is the relationship between growth rate and growth factor?

Back

The growth factor can be calculated as (1 + r), where r is the growth rate expressed as a decimal.

Tags

CCSS.HSF-IF.C.8B

Front

If a quantity increases by 15% each year, what is the growth factor?

Back

The growth factor is 1.15, calculated as (1 + 0.15).

Tags

CCSS.HSF-IF.C.8B