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during the first years of growth the height of a tree can be modeled with the function h=-t^2 +12t+10 where t is the time in years since being planted and h is the height in inches. Enter the average rate cof change, in inches per year, from year 1 to year 5.

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ANSWER

6 inches

EXPLANATION

The given function is

[tex]h(t) = - {t}^{2} + 12t + 10[/tex]

The average rate of change from t=1 to t=5 is given by:

[tex] = \frac{h(5) - h(1)}{5 - 1} [/tex]

[tex]h(5) = - {(5)}^{2} + 12(5) + 10[/tex]

[tex]h(5) = - 25 + 60+ 10[/tex]

[tex]h(5) = 45[/tex]

Also,

[tex]h(1) = - {(1)}^{2} + 12(1) + 10[/tex]

[tex]h(1) = - 1+ 12+ 10[/tex]

[tex]h(1) = 21[/tex]

The average rate of change is now

[tex] = \frac{45 - 21}{4} [/tex]

[tex] = \frac{24}{4} [/tex]

[tex] = 6[/tex]

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