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Answer:
The average rate of change is 7.
Step-by-step explanation:
We are given the function:
[tex]f(x)=2x^2+x+5[/tex]
Which represents the number of jars of pickles, y (in tens of jars), Denise expects to sell x weeks after launching her store.
We want to find the average rate of change over 1 ≤ x ≤ 2.
Essentially, we want to find the slope over f(1) and f(2).
Thus, first evaluate the two endpoints:
[tex]f(1)=2(1)^2+(1)+5=2+1+5=8[/tex]
And:
[tex]f(2)=2(2)^2+2+5=8+2+5=15[/tex]
This gives us the two points (1, 8) and (2, 15).
Then the average rate of change will be the slope between the two:
[tex]\displaystyle m=\frac{15-8}{2-1}=7[/tex]
With units, this means that over the first and second week, Denise sold on average 70 jars of pickles per week.