Exponential Growth and Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, leading to rapid increases as the base amount grows.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to rapid decreases as the base amount shrinks.

Front

How do you calculate compound interest?

Back

Compound interest can be calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is N(t) = N0 * e^(rt), where N(t) is the amount at time t, N0 is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is N(t) = N0 * e^(-rt), where N(t) is the amount at time t, N0 is the initial amount, r is the decay rate, and t is time.

Front

If a population of 1000 increases by 10% each year, what will it be after 3 years?

Back

After 3 years, the population will be approximately 1331.

Front

If a substance decays by 25% each year, what fraction remains after 2 years?

Back

After 2 years, 56.25% of the substance remains.

Front

What does it mean for a quantity to decrease by a percentage?

Back

It means that the quantity is reduced by that percentage of its current value each time period.

Front

How do you find the remaining quantity after multiple years of decay?

Back

You can use the formula N(t) = N0 * (1 - r)^t, where N0 is the initial quantity, r is the decay rate, and t is the number of years.

Front

What is the significance of the base 'e' in exponential functions?

Back

The base 'e' (approximately 2.718) is a mathematical constant that is the limit of (1 + 1/n)^n as n approaches infinity, and it is used in continuous growth and decay models.