Exponential Growth and Decay Review

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over a period of time, represented by the equation y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over a period of time, represented by the equation y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

Identify the growth factor in the equation y = 3(1.2)^x.

Back

The growth factor is 1.2.

Front

Identify the decay factor in the equation y = 205(0.25)^x.

Back

The decay factor is 0.25.

Front

What does the y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value or starting amount of the quantity before any growth or decay occurs.

Front

In the equation y = 21(1.13)^x, what is the initial value?

Back

The initial value is 21.

Front

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

Back

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

Front

Calculate f(2) for the function f(x) = 30(1.5)^x.

Back

f(2) = 30(1.5)^2 = 30(2.25) = 67.5.

Front

What is the general form of an exponential growth equation?

Back

The general form is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the general form of an exponential decay equation?

Back

The general form is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.