Exponential Word Problems 21-22

Front

What is the formula to calculate the equivalent annual interest rate from a monthly interest rate?

Back

The equivalent annual interest rate can be calculated using the formula: (1 + monthly rate)^12 - 1.

Front

If a car's value is $15,000 and it depreciates at 8% per year, what is the exponential decay equation for its value?

Back

y = 15,000(0.92)^x, where x is the number of years.

Front

How do you estimate future population using continuous growth rate?

Back

Use the formula: P = P0 * e^(rt), where P0 is the initial population, r is the growth rate, and t is time in years.

Front

What is the formula for compound interest when compounded semiannually?

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 is the annual growth rate if a house's value increases from $80,000 to $258,000 over 24 years?

Back

The annual growth rate can be calculated using the formula: r = (Final Value/Initial Value)^(1/t) - 1.

Front

What does it mean for an interest rate to be compounded semiannually?

Back

It means that the interest is calculated and added to the principal twice a year.

Front

How do you convert a percentage growth rate to a decimal for calculations?

Back

Divide the percentage by 100. For example, 5% becomes 0.05.

Front

What is the significance of the number 'e' in continuous growth models?

Back

The number 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth and decay models.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage.

Front

How can you determine the future value of an investment with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt) to calculate the future value.