Question

determine the base of the function $y = -7(19)^x$, and state if the function is classified as exponential growth or decay.

• the base is 19, and the function is classified as exponential growth.
• the base is -7, and the function is classified as exponential growth.
• the base is 19, and the function is classified as exponential decay.
• the base is -7, and the function is classified as exponential decay

Explanation:

The general form of an exponential function is \( y = a(b)^x \), where \( b \) is the base. In the function \( y = -7(19)^x \), comparing with the general form, the base \( b \) is 19. For exponential growth or decay, if the base \( b>1 \), it is exponential growth (since as \( x \) increases, \( b^x \) increases). Here, \( 19 > 1 \), so the function is exponential growth.

Answer:

A. The base is 19, and the function is classified as exponential growth.