Question

what is the base of the function $y = 7(1.35)^x$? is the function classified as exponential growth or decay?

• the base is 7, and the function is classified as exponential growth.
• the base is 1.35, and the function is classified as exponential growth.
• the base is 7, and the function is classified as exponential decay.
• the base is 1.35, and the function is classified as exponential decay

Explanation:

The general form of an exponential function is \( y = a(b)^x \), where \( a \) is the initial value and \( b \) is the base. For \( y = 7(1.35)^x \), comparing with the general form, the base \( b \) is \( 1.35 \). An exponential function is growth if \( b>1 \) and decay if \( 0 < b < 1 \). Since \( 1.35>1 \), it is exponential growth.

Answer:

B. The base is 1.35, and the function is classified as exponential growth