Exponential Growth and Decay Applications

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Tags

CCSS.HSF-IF.C.8B

Front

Write the general formula for exponential growth.

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

Write the general formula for exponential decay.

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

What does the base of an exponential function represent?

Back

The base indicates the growth or decay factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

The growth factor is 2, as the population doubles.

Tags

CCSS.HSF-LE.A.1A

Front

How do you calculate the percent increase in an exponential function?

Back

Percent increase = (final value - initial value) / initial value * 100%.

Tags

CCSS.HSF-LE.A.1C

Front

How do you calculate the percent decrease in an exponential function?

Back

Percent decrease = (initial value - final value) / initial value * 100%.

Tags

CCSS.HSF-LE.A.1C

Front

What is the formula for continuous compounding?

Back

A = Pe^(rt), where 'A' is the amount, 'P' is the principal, 'e' is Euler's number, 'r' is the rate, and 't' is time.

Front

What is the half-life in exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value.