Question

over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?
( x = 0 ) to ( x = 2 )
( x = 0 ) to ( x = 1.79 )
( x = 0.58 ) to ( x = 1.79 )
( x = 1.79 ) to ( x = 3 )

Explanation:

Step1: Analyze the intersection point

The intersection point of the exponential function and the linear function is at \(x = 1.79\). Before the intersection point, the exponential function has a greater growth rate.

Step2: Determine the interval

We need to find the interval where the exponential function's growth rate exceeds the linear function's. Since the intersection is at \(x = 1.79\), the interval starts from the \(x\) - value where the exponential function starts to be compared (assuming it starts at \(x = 0\)) and ends at \(x = 1.79\).

Answer:

\(x = 0\) to \(x = 1.79\)