Question

A spring is being stretched by a weight d(t)= 100t/2t+15

find the average rate of change on interval (21,26)
find the average rate of change on interval (25,26)
find the average rate of change on interval (25.9,26)

Answer 1

To calculate the average rate of change for the function d(t)= 100t/2t+15 over various intervals, you use the formula [d(b) - d(a)] / (b - a), plugging in the respective values of the function at the ends of the intervals.

Step-by-step explanation:

To find the average rate of change of a function d(t) on an interval [a, b], you use the formula:

Average rate of change = [d(b) - d(a)] / (b - a)

For the function d(t)= 100t/2t+15, you would substitute the values of t from the intervals to find d(a) and d(b) respectively, and then plug them into the formula.

1. For the interval (21,26), calculate d(21) and d(26), then use the formula to find the average rate of change.
2. Repeat the process for the interval (25,26).
3. Finally, do the same for the interval (25.9,26).

Note that as the interval narrows, the average rate of change approaches the instantaneous rate of change, which would be the derivative of the function d(t) at that point.