Exponential Growth/Decay

Front

What is the general form of an exponential growth equation?

Back

y = a(b)^x, where a is the initial amount and b is the growth factor (b > 1).

Front

What is the general form of an exponential decay equation?

Back

y = a(b)^x, where a is the initial amount and 0 < b < 1.

Front

What does the common ratio in an exponential function represent?

Back

The factor by which the quantity increases or decreases in each time period.

Front

How do you determine the growth factor from an exponential function?

Back

The growth factor is the base of the exponent in the equation y = a(b)^x.

Front

What is the significance of the exponent in an exponential function?

Back

The exponent represents the number of time periods that have passed.

Front

How can you express the size of an object that doubles in size every week mathematically?

Back

Using the expression y = initial size * (2)^t, where t is the number of weeks.

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

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

Back

Use the formula A = P(1 + r)^t, where A is the future value, P is the principal, r is the annual interest rate, and t is the number of years.

Front

What is the effect of increasing the interest rate on the future value of an investment?

Back

Increasing the interest rate will increase the future value of the investment.

Front

What is the relationship between exponential functions and their graphs?

Back

Exponential growth functions rise sharply, while exponential decay functions fall rapidly.