If the function h(x)=2x2+5 models the number of apples on an apple tree x weeks after it was fertilized, calculate the average rate of change in apples between weeks 2 and 6.

Answer 1

To calculate the average rate of change in apples between weeks 2 and 6, we need to find the difference in the number of apples between week 6 and week 2, and then divide this difference by the change in weeks.

First, calculate the number of apples at week 2 and week 6 using the function h(x)=2x^2+5:

At week 2:
h(2) = 2(2^2) + 5
h(2) = 2(4) + 5
h(2) = 8 + 5
h(2) = 13

At week 6:
h(6) = 2(6^2) + 5
h(6) = 2(36) + 5
h(6) = 72 + 5
h(6) = 77

Next, calculate the difference in the number of apples between week 6 and week 2:

Difference = Number of apples at week 6 - Number of apples at week 2
Difference = 77 - 13
Difference = 64

The change in weeks is from week 2 to week 6, which is 6 - 2 = 4 weeks.

Therefore, the average rate of change in apples between weeks 2 and 6 is:

Average rate of change = Difference in number of apples / Change in weeks
Average rate of change = 64 / 4
Average rate of change = 16

So, the average rate of change in apples between weeks 2 and 6 is 16 apples per week.