POSSIBLE SOLUTION(S)

1. Piecewise linear graph of the data.

2. We are looking for the time at which the rate of transfer of energy to the bat is increasing at the fastest. From the graph, it appears that the largest rate of increase is between t = .1 seconds and t = .125 seconds.

3. Use the trapezoid rule to estimate the area under the graph which represents the total energy transferred to the bat in a given time interval. Be certain to label the units of measure for total energy transferred.

4. Find a polynomial function which fits this data.

5. The energy transfer is increasing at the fastest rate when its change (derivative) is maximized. That happens when the second derivative is zero while the first derivative is positive.

6. The cumulative energy transfer is found by summing the power*time so the desired function which we call g[x] is the integral of x from time t=0 to t=x.