Growth rate of a tubeworm: A study of the growth rate and life span of a marine tubeworm concludes that it is the longest-lived noncolonial marine invertebrate known.9 Since tubeworms live on the...

Growth rate of a tubeworm: A study of the growth rate and life span of a marine tubeworm concludes that it is the longest-lived noncolonial marine invertebrate known.9 Since tubeworms live on the ocean floor and have a long life span, scientists do not measure their age directly. Instead, scientists measure their growth rate at various lengths and then construct a model for growth rate in terms of length. On the basis of that model, scientists can find a relationship between age and length. This is a good example of how rates of change can be used to determine a relationship when direct measurement is difficult or impossible. The table following shows for a tubeworm the rate of growth in length, measured in meters per year, at the given length, in meters.

a. Often in biology the growth rate is modeled as a decreasing linear function of length. For some organisms, however, it may be appropriate to model the growth rate as a decreasing exponential function of length. Use the data in the table to decide which model is more appropriate for the tubeworm, and find that model. Give a practical explanation of the slope or percentage decay rate, whichever is applicable.

b. Use functional notation to express the growth rate at a length of 0.64 meter, and then calculate that value using your model from part a.