Question

A linear function and an exponential function are shown below:

Linear function: y = 5 + 4x
Exponential function: N = 3 × (2)x

Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?

A) x > -1
B) x > 0
C) x > 1
D) x > 2

Answer 1

The growth rate of the exponential function exceeds the growth rate of the linear function over the interval x > 0.

Step-by-step explanation:

To compare the growth rates, we can examine the exponents in both functions. The exponential function
`N = 3 * 2^x\)` has a base of 2 raised to the power of x, indicating exponential growth. In contrast, the linear function y = 5 + 4x has a constant growth rate represented by the coefficient 4.

For the exponential function to exceed the linear function's growth rate, we need the exponent in the exponential function to be greater than the coefficient of x in the linear function. In this case, xneeds to be greater than 0. Therefore, the correct interval is x > 0.

In conclusion, the exponential function surpasses the linear function's growth rate for x greater than 0, making option B) x > 0 the correct choice for the interval where the exponential function's growth rate exceeds that of the linear function.