Answer:
To find the average rate of change of the function h(t) = t + 3^t on the interval 1/2 ≤ t ≤ 1, we can use the formula:
Average Rate of Change = (h(1) - h(1/2))/(1 - 1/2)
First, let's find h(1) and h(1/2):
h(1) = 1 + 3^1 = 1 + 3 = 4
h(1/2) = 1/2 + 3^(1/2) = 1/2 + √3 ≈ 1/2 + 1.732 ≈ 2.232
Now, substitute the values into the formula:
Average Rate of Change = (4 - 2.232)/(1 - 1/2)
= 1.768/1/2
= 1.768 * 2
= 3.536
Therefore, the average rate of change of the function h(t) = t + 3^t on the interval 1/2 ≤ t ≤ 1 is approximately 3.536.
