the graph below shows an exponential function and a quaractic function.

how do the functions compare over the interval
0<_ x<_1?

A. the exponential grows at approximately half the rate of the quadratic
B. the exponential grows at approximately the same rate as the quadratic
C.the exponential grows at approximately twice the rate of the quadratic
D.the exponential grows at approximately four times the rate of the quadratic

please help i’m begging times :(

The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

Average rate of change of a function A = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.

A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by

[tex]\frac{f(b)-f(a)}{b-a}[/tex].

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by

[tex]\frac{f(1)-f(0)}{1-0}[/tex] = [tex]\frac{2-1}{1}[/tex] = 1

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by

[tex]\frac{g(1)-g(0)}{1-0}[/tex] = [tex]\frac{1-0}{1}[/tex] = 1

Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.

Find out more information about average Rate of Change function here

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