Exponential Growth and Decay

Front

What is Exponential Growth?

Back

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

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.

Front

Write the general formula for an exponential growth function.

Back

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

Front

Write the general formula for an exponential decay function.

Back

y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time.

Front

If a quantity doubles every year, what is the growth factor?

Back

The growth factor is 2.

Front

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

Back

The decay factor is 0.8.

Front

How do you identify an exponential growth function from a formula?

Back

An exponential growth function has a base greater than 1 in the form y = a(b)^x, where b > 1.

Front

How do you identify an exponential decay function from a formula?

Back

An exponential decay function has a base between 0 and 1 in the form y = a(b)^x, where 0 < b < 1.

Front

What does the variable 'x' represent in exponential functions?

Back

The variable 'x' represents the time period or number of intervals.

Front

What is the initial value in the function y = 1400(1.09)^x?

Back

The initial value is 1400.