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.

Tags

CCSS.HSF-LE.A.1A

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.

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF-LE.A.1A

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.

Tags

CCSS.HSF-LE.A.1A

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.

Tags

CCSS.HSF-LE.A.1C

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.

Tags

CCSS.HSF-LE.A.1C

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.

Tags

CCSS.HSF-LE.A.1C

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.

Tags

CCSS.HSF-IF.C.8B