A6 - Exponential Growth and Decay Word Problems

Front

What is an exponential growth function?

Back

An exponential growth function is a mathematical expression that describes a quantity increasing at a constant percentage rate over time, typically represented as y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

What is an exponential decay function?

Back

An exponential decay function describes a quantity decreasing at a constant percentage rate over time, typically represented as y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

How do you identify exponential growth from a function?

Back

Exponential growth is identified by a base greater than 1 in the function y = a(1 + r)^x.

Front

How do you identify exponential decay from a function?

Back

Exponential decay is identified by a base between 0 and 1 in the function y = a(1 - r)^x.

Front

What does a growth rate of 9% mean in an exponential function?

Back

A growth rate of 9% means that the quantity increases by 9% of its current value each time period.

Front

If a quantity decreases by 7% each year, what is the decay factor?

Back

The decay factor is 0.93, calculated as 1 - 0.07.

Front

Write an exponential growth function for a quantity that starts at 100 and grows by 14% per time period.

Back

y = 100(1.14)^x.

Front

Write an exponential decay function for a quantity that starts at 500 and decays by 5% per time period.

Back

y = 500(0.95)^x.

Front

What is the value of a $12,500 boat after 8 years if it depreciates by 7% annually?

Back

$6,994.77.

Front

How do you calculate the future value of an investment using exponential growth?

Back

Use the formula y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the number of time periods.