Question

PLEASEE HELPP ANYONE

A linear function and an exponential function are shown below.
Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?
A X<1
B 0 IS LESS THAN EQUAL TO X IS LESS THAN OR = TO 1
C 1 IS LESS THAN OR = TO X IS LESS THAN OR = TO 2
D X >2

Answer 1

D is correct. x>2 the growth rate of the exponential function exceed the growth rate of the linear function.

Explanation:

We are given a linear function and an exponential function in graph.

We need to find interval when growth rate of the exponential function exceed the growth rate of the linear function.

`\text{Linear function: }L(x)=2x`

`\text{Exponential function: }E(x)=2^x`

Option A) When x<1

Growth rate of linear function = 2

Growth rate of Exponential function = 0.75

When x<1 , growth rate of exponential function is less than linear function.

Option B) When 0≤x≤1

Growth rate of linear function = 2

Growth rate of Exponential function = 1

When 0≤x≤1 , growth rate of exponential function is less than linear function.

Option C) When 1≤x≤2

Growth rate of linear function = 2

Growth rate of Exponential function = 2

When 1≤x≤2 , growth rate of exponential function is equal to linear function.

Option D) When x>2

Growth rate of linear function = 2

Growth rate of Exponential function = 4

When x>2 , growth rate of exponential function is exceed the growth rate of linear function.

Thus, x>2 the growth rate of the exponential function exceed the growth rate of the linear function.

Answer 2

Answer: D) x>2.

This is because the slope of the exponential function is clearly greater than the linear function from 2 on the x=axis forward.