Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate. For example, if a population grows by 25% each month, it will grow faster each month as the base number increases.

Front

What is exponential decay?

Back

Exponential decay is the decrease in a quantity at a rate proportional to its current value, resulting in a rapid decline. For instance, if a population decreases by 30% each year, it will lose a larger number of individuals each year as the base number decreases.

Front

How do you calculate the future value in exponential growth?

Back

The future value can be calculated using the formula: FV = P(1 + r)^t, where FV is the future value, P is the present value, r is the growth rate, and t is the time period.

Front

How do you calculate the future value in exponential decay?

Back

The future value can be calculated using the formula: FV = P(1 - r)^t, where FV is the future value, P is the present value, r is the decay rate, and t is the time period.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = P(1 + r)^t, where y is the future amount, P is the initial amount, r is the growth rate, and t is the time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = P(1 - r)^t, where y is the remaining amount, P is the initial amount, r is the decay rate, and t is the time.

Front

If a population of 4,000 mosquitoes grows at a rate of 25% per month, how many mosquitoes will there be after 4 months?

Back

9765 mosquitoes.

Front

If a printer worth $35,000 depreciates at a rate of 15% per year, how long will it take for its value to drop by $5,000?

Back

0.948 years.

Front

A fish population starts at 8,000 and decreases by 1.6% per month. What is the population after 2 years?

Back

5432.157 fish.

Front

Write the equation for a bacteria culture that starts with 5000 cells and dies by 30% each year.

Back

y = 5000(0.7)^x.