Intro to 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. Example: A population of bacteria doubles every hour.

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. Example: A radioactive substance decaying over time.

Front

Write an expression for a quantity that doubles every week starting from 50.

Back

50(2)^t, where t is the number of weeks.

Front

What does the base in an exponential function represent?

Back

The base represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

Front

How do you identify an exponential growth function?

Back

An exponential growth function has a form A = P(1 + r)^t, where r > 0.

Front

How do you identify an exponential decay function?

Back

An exponential decay function has a form A = P(1 - r)^t, where r > 0.

Front

What is the general form of an exponential function?

Back

The general form is A = Pe^kt, where A is the amount, P is the initial amount, k is the growth/decay rate, and t is time.

Front

If a population of 200 decreases by 10% each year, what is the expression for the population after t years?

Back

200(0.9)^t.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What is the value of 2³?

Back

8.