Question

an exponential function and a linear function are graphed. over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function? options: x=0 to x=3; x=1.79 to x=3; x=0.38 to x=1.79; x=0 to x=1.79

Explanation:

To determine when the exponential function's growth rate exceeds the linear function's, we analyze the graph. The two functions intersect at \((1.79, 7.17)\). For \(x > 1.79\), the exponential function (which grows faster over time) will have a steeper slope (higher growth rate) than the linear function. So we check the intervals:

• \(x = 0\) to \(x = 3\): Includes both before and after the intersection, not specific to when exponential exceeds.
• \(x = 1.79\) to \(x = 3\): After the intersection point, exponential's growth rate (slope) becomes greater than linear's.
• \(x = 0.38\) to \(x = 1.79\): Before or at intersection, linear may be equal or faster.
• \(x = 0\) to \(x = 1.79\): Before intersection, linear or equal growth.

Answer:

\(x = 1.79\) to \(x = 3\)