Cyclist is riding less each week before the race
Answer:
A. -15.2%
B. negative percent rate of change indicates a deliberate reduction in weekly training mileage to prepare effectively for the cycling road race.
Explanation:
1. We start with the function:
d(t) = 150* (0.85)^t
2. Find the derivative of d(t) with respect to t using the power rule and the chain rule for exponential functions:
d'(t) = 150* In(0.85)* (0.85)^t
3. Express the result as a percentage rate of change:
Percent Rate of Change = (d'(t) / d(t)) * 100
4. Plug in the values for d'(t) and d(t):
Percent Rate of Change = [150* In(0.85)* (0.85)^t] / [150* (0.85)^t]* 100
5. Simplify the expression by canceling out the "150" and "(0.85)^t" terms:
Percent Rate of Change = In(0.85)*100
6. Calculate the value:
Percent Rate of Change = -15.2%
So, the percent rate of change in the context of the problem is approximately -15.2%. This means that the weekly training mileage is decreasing by about 15.2% each week as the cyclist approaches the cycling road race.
Part B: Explain the meaning of the percent rate of change in the context of the problem.
In the context of the problem, the percent rate of change represents how the cyclist is adjusting their weekly training mileage in preparation for the upcoming cycling road race. Specifically, the percent rate of change is approximately -15.2%.
Here's the meaning of the percent rate of change:
- A negative rate of change (-15.2%) indicates a decrease in the weekly training mileage over time. In other words, as the number of weeks leading up to the race increases, the cyclist is reducing the distance they ride each week.
- This reduction in training mileage is likely part of a tapering strategy commonly used by athletes before important events. Tapering involves gradually decreasing the training workload to allow the body to recover, reduce fatigue, and peak in performance for the race.
- The cyclist is not maintaining a consistent weekly training distance but is progressively reducing it. This approach aims to optimize performance for the road race by ensuring that the cyclist is well-rested and in peak physical condition on the race day.
So, in summary, the negative percent rate of change indicates a deliberate reduction in weekly training mileage to prepare effectively for the cycling road race.