Question

comparing the linear and exponential functions, which has the greatest rate of change as x increases?
a. the linear function has the greatest rate of change.
b. the exponential function has the greatest rate of change

Explanation:

Step1: Analyze Linear Rate

Linear functions have a constant rate of change (slope). From the graph, the blue line (linear) has a steady, non - accelerating slope.

Step2: Analyze Exponential Rate

Exponential functions have a rate of change that increases (for growth) as \(x\) increases. The red curve (exponential) is curving upwards, meaning its rate of change (derivative for exponential functions, or the steepness of the curve) is increasing as \(x\) gets larger. Visually, as \(x\) increases, the exponential curve becomes steeper than the linear line.

Answer:

B. The exponential function has the greatest rate of change