Question

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.

Answer 1

6 inches

Step-by-step explanation

The given function is

`h(t) = - {t}^(2) + 12t + 10`

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

`= (h(5) - h(1))/(5 - 1)`

`h(5) = - {(5)}^(2) + 12(5) + 10`

`h(5) = - 25 + 60+ 10`

`h(5) = 45`

Also,

`h(1) = - {(1)}^(2) + 12(1) + 10`

`h(1) = - 1+ 12+ 10`

`h(1) = 21`

The average rate of change is now

`= (45 - 21)/(4)`

`= (24)/(4)`

`= 6`