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, leading to rapid increases. Example: A population growing at 10% per year.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time. Example: A radioactive substance losing 20% of its mass every year.

Front

What is the decay factor if the decay rate is 20%?

Back

0.8 (100% - 20% = 80%, or 0.8 as a decimal).

Front

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

Back

Future Value = Principal × (1 + interest rate)^number of years.

Front

What is the formula for Exponential Growth?

Back

A = P(1 + r)^t, where A is the amount, P is the principal, r is the growth rate, and t is time.

Front

What is the formula for Exponential Decay?

Back

A = P(1 - r)^t, where A is the amount, P is the principal, 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

9765 mosquitoes.

Front

What type of function is y = 7(5/4)^x?

Back

Exponential Growth.

Front

What does a decay rate of 30% imply about the decay factor?

Back

The decay factor is 0.7 (100% - 30% = 70%, or 0.7 as a decimal).

Front

If an investment of $600 earns 5% interest compounded annually, how much will it be worth after 5 years?

Back

$765.77.