Exponential growth rate and generation time: In this exercise, we will examine the relationship between a population’s intrinsic exponential growth rate r and the generation time T —that is, the time...

Exponential growth rate and generation time: In this exercise, we will examine the relationship between a population’s intrinsic exponential growth rate r and the generation time T —that is, the time it takes an organism to reach reproductive maturity. The following table gives values of the generation time and the exponential growth rate for a selection of lower organisms.37 The basic unit of time is a day.

a. By plotting ln r against ln T , determine whether it is reasonable to model r as a power function of T.

b. Find a formula for the regression line of ln r against ln T. (Round the slope to one decimal place.)

c. Find a formula that modelsr as a power function of T , and make a graph of this function. (Use a horizontal span from 0 to 10.)

d. we found a power relation between generation time T , in years, and length L. Use this relation and the results of part c to find a formula for r as a function of length L for this group of lower organisms. (Convert the power relation from to measure time in days, and remember that T −1 = 1/T.)