Question

the graph of the function f(x)=35cdot2^{x} is shown below. which of the following best describes the behavior of this function? a the function decreases quickly at first, then continues to decrease more slowly as x increases. b the function decreases at first, then increases as x increases. c the function grows more rapidly as x increases. d the function grows at a constant rate as x increases.

Explanation:

Step1: Analyze the graph

The graph of the function \(y = 35\cdot2^{x}\) is an exponential - decay function. As \(x\) increases, the function value \(y\) decreases. At the beginning (for smaller \(x\) values), the function value changes more rapidly, and as \(x\) gets larger, the rate of decrease slows down.

Answer:

A. The function decreases quickly at first, then continues to decrease more slowly as \(x\) increases.