3.5 Applications of Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a consistent time period, resulting in a rapid increase.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a consistent time period, leading to a rapid decrease.

Front

How do you calculate the future value in exponential growth?

Back

Use the formula: Future Value = Initial Value × (1 + growth rate)^time.

Front

How do you calculate the future value in exponential decay?

Back

Use the formula: Future Value = Initial Value × (1 - decay rate)^time.

Front

What is the growth rate in the function y = 1400(1.09)^x?

Back

The growth rate is 9% per year.

Front

What is the decay rate in the function y = 300(0.91)^x?

Back

The decay rate is 9% per year.

Front

What does the initial value represent in an exponential function?

Back

The initial value is the starting amount before any growth or decay occurs.

Front

What is the formula for exponential growth?

Back

The formula is y = a(1 + r)^t, where a 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 y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

If a population of 4,000 mosquitoes grows at 25% per month, how many will there be after 4 months?

Back

There will be 9766 mosquitoes after 4 months.