Final answer:
To determine the average rate of change of the function T(x) over the interval [10, 30], calculate the function values at the endpoints, subtract them, and divide by the change in x. The average rate of change is approximately -6.05 degrees per minute, making the correct answer Option A.
Step-by-step explanation:
To find the average rate of change of the function T(x) = 15 + 155e-0.02x over the interval [10, 30], we need to calculate the difference in function values at these points and divide it by the difference in x-values.
- First, calculate T(10) and T(30).
- Then find the difference: T(30) - T(10).
- Finally, divide by the change in x: (T(30) - T(10))/(30 - 10).
Here are the calculations:
T(10) = 15 + 155e-0.02(10) = 15 + 155e-0.2
T(30) = 15 + 155e-0.02(30) = 15 + 155e-0.6
Now subtract the lower x-value function from the higher, and divide by the number of units between the two x-values:
Average Rate of Change = (T(30) - T(10)) / (30 - 10)
Plugging in the values we get:
Average Rate of Change = ((15 + 155e-0.6) - (15 + 155e-0.2)) / 20
Calculating the numerical values (using a calculator):
Average Rate of Change ≈ (-6.05) degrees per minute
Therefore, the correct answer is Option A, which is approximately -6.05 degrees per minute.