Question

determine the base of the function \\(y = 18(1.4)^x\\), and state if the function is classified as exponential growth or decay.

the base is 1.4, and the function is classified as exponential decay.
the base is 1.4, and the function is classified as exponential growth.
the base is 18, and the function is classified as exponential decay.
the base is 18, and the function is classified as exponential growth.

Explanation:

Identify the base of the exponential function

The given function is:

$$y = 18(1.4)^x$$

An exponential function is written in the form \(y = a(b)^x\), where \(b\) is the base.
Comparing the equations:

$$b = 1.4$$

Classify as growth or decay

For an exponential function \(y = a(b)^x\) with \(a > 0\):

• If \(b > 1\), the function represents exponential growth.
• If \(0 < b < 1\), the function represents exponential decay.

Since \(1.4 > 1\), the function is classified as exponential growth.

Answer:

• The base is 1.4, and the function is classified as exponential decay.
• The base is 1.4, and the function is classified as exponential growth. (Correct answer)
• The base is 18, and the function is classified as exponential decay.
• The base is 18, and the function is classified as exponential growth.