1 Answer

Tim Morgan · Answer 1 · 2023-11-11T08:52:14+0000

STEP - BY - STEP EXPLANATION

What to find?

Determine how much greater the average rate of change over the interval [ 7, 9] than the interval [4, 6].

Given:

Step 1

Calculate the average rate of change over the interval [ 7, 9] using the formula below:

$Rate\text{ of change=}(f(b)-f(a))/(b-a)$

a= 7 f(a)=1852

b=9 f(b)=3878

Substitute the values into the formula and simplify.

$Average\text{ rate of change=}(3878-1852)/(9-7)$
=(2026)/(2)=1013

Step 2

Calculate the average rate of change over the interval [4, 6] using the same formula in step 2.

a=4 f(a)=358

b=6 f(b)=1178

$average\text{ rate of change=}(1178-358)/(6-4)$
=(820)/(2)=410

Step 3

Compare the average rate of change over the two intervals.

Clearly, the average rate of change over the the interval [7, 9] is greater than the average rate of change over the interval [4, 6].

ANSWER

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