Question

19

Answer 1

The function with the greatest average rate of change is the function k(x)

How to determine the function?

The average rate of change is calculated as

$m = \frac{y_2 - y_1}{x_2 -x_1}$

The interval is [0,2].

So, we have

$m = \frac{y_2 - y_1}{2 -0}$

$m = \frac{y_2 - y_1}{2}$

For function j(x), we have

j(2) = 3 * 1.6^2 = 7.68

j(2) = 3 * 1.6^0 = 3

So, we have

$m_j = \frac{7.68 - 3}{2}$

$m_j = 2.34$

For function g(x), we have

g(2) = 25/2

g(0) = 8

So, we have

$m_g = \frac{25/2 - 8}{2}$

$m_g = 2.25$

For function k(x), we have

k(2) = 9

k(0) = 4

So, we have

$m_k = \frac{9 - 4}{2}$

$m_k = 2.5$

For function f(x), we have

f(2) = 1.5 * 2^2 = 6

f(0) = 1.5

So, we have

$m_f = \frac{6 - 1.5}{2}$

$m_f = 2.25$

The function with the greatest average rate of change is the function k(x) with a rate of 2.5

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