A6 - Exponential Growth and Decay Word Problems

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.

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.

Front

How do you identify exponential growth or decay in a word problem?

Back

Look for keywords indicating increase (growth) or decrease (decay) and check if the rate is a percentage.

Front

What is the formula for exponential growth?

Back

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

Front

If a population increases by 4% each year, what is the growth factor?

Back

The growth factor is 1.04.

Front

If a population decreases by 4.5% each year, what is the decay factor?

Back

The decay factor is 0.955.

Front

How do you calculate the future value of an investment with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the approximate value of an investment of $30,000 after 51 years at a 5% annual growth rate?

Back

Approximately $344,022.

Front

What does the term 'compounded quarterly' mean?

Back

It means that the interest is calculated and added to the principal four times a year.