## Developing a Working Formula for Energy

Equation 5 gives us what seems like a reasonable formula. However, we are not interested in what happens when one crow tries to break one whelk open; we are interested in what happens in general. We can generalize equation 5 by using the data Zach gathered in Table 1, which gave the average number of drops it took to break whelks from particular heights.

To start, let's graph equation 5 for all the different heights that Zach tried, using the steps in exercise 4.

Exercise 4: Answer the following questions:

a) What shape would the graph of E = HN be, where E is a function of N, and H is a constant (Hint: consider the shape of y = 5x, for example)?

b) On a large grid, sketch the graph of energy expended versus number of drops, for a height of 6 metres.

c) Consider where the curves E = 10N and E = 2N should be, relative to the curve E = 6N you drew in part (b). Here's a hint: if a crow is flying higher up for each drop, it will expend more energy for each drop. Sketch these on the same grid.

d) For H = 3,4,5,7,8,15, use the logic from part (c) to sketch E = HN on the same grid.