Question

Given the linear and exponential functions shown below:

SER654+(2,4)3+2+(1,2)0.0−2−1(0,0)23
Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?
A) x<1
B) 0≤x≤1
C) 1≤x≤2
D) x>2

Answer 1

The growth rate of the exponential function exceeds the growth rate of the linear function for all values of x in the given interval.

Step-by-step explanation:

The growth rate of an exponential function exceeds the growth rate of a linear function over an interval where the exponential function is increasing at a faster rate. Since the exponential function is always increasing, its growth rate is always positive. On the other hand, the growth rate of a linear function is constant. Therefore, the growth rate of the exponential function exceeds the growth rate of the linear function for all values of x in the given interval.