PRACTICE 3.3: Applications Exponential Growth/Decay and Compound Interest

Front

What is the formula for compound interest?

Back

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

Front

What does 'semi-annually' mean in terms of compounding frequency?

Back

Semi-annually means that interest is compounded twice a year.

Front

How do you calculate the future value of an investment using exponential growth?

Back

Use the formula: A = P(1 + r)^t, where A is the future value, P is the principal, r is the growth rate, and t is the time in years.

Front

What is exponential decay?

Back

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Front

What is the formula for exponential decay?

Back

y = a(1 - r)^t, where y is the remaining amount, a is the initial amount, r is the decay rate, and t is the time.

Front

If a quantity halves every year, what is the decay factor?

Back

The decay factor is 0.5.

Front

What is the value of an investment of $400 after 5 years at an interest rate of 4.29% compounded annually?

Back

y = 400(1 + 0.0429)^5 = $490.73.

Front

What is the depreciation formula for an asset?

Back

Value = Initial Value * (1 - Depreciation Rate)^t.

Front

If a printer worth $35,000 depreciates at 5% per year, what will it be worth after 8 years?

Back

Value = 35000 * (1 - 0.05)^8 = $23,219.72.

Front

What is the expression for a quantity that doubles every week?

Back

If the initial quantity is Q, the expression is Q(2)^t, where t is the number of weeks.