Exponential Word Problems

Front

What is the formula for compound interest?

Back

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 does it mean for an investment to double?

Back

An investment doubles when its value becomes twice the original amount.

Front

How do you determine if a function represents exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

Front

What is the continuous compounding formula?

Back

A = Pe^(rt), where A is the amount, P is the principal, r is the annual interest rate, t is the time in years, and e is Euler's number (approximately 2.71828).

Front

If $3000 is invested at 3% compounded continuously, how long will it take to double?

Back

It will take approximately 23.1 years.

Front

What is the growth rate in the equation P = 3400(1 + 0.03)^t?

Back

The growth rate is 3% per year.

Front

How do you calculate the future value of an investment compounded monthly?

Back

Use the formula A = P(1 + r/n)^(nt), substituting n with 12 for monthly compounding.

Front

What is the principal in the context of an investment?

Back

The principal is the initial amount of money invested or loaned.

Front

What is the significance of the number 1.2 in exponential growth?

Back

A base greater than 1 (like 1.2) indicates growth; the investment or population is increasing.

Front

How do you find the time it takes for an investment to reach a certain amount?

Back

You can use logarithms to solve for t in the equation A = Pe^(rt) or A = P(1 + r/n)^(nt).