3.17 In a study to develop the growth behavior for protozoa colonization in a particular lake, an experiment was conducted in which 15 sponges were placed in a lake and 3 sponges at a time were gathered. Then the number of protozoa were counted at 1, 3, 6, 15, and 21 days. In this case the MacArthur-Wilson equation was used to describe the growth mechanism. The model is given by y = ßdl-e-k')

where y = total protozoa on the sponge βι = species equilibrium constant 2 = parameter that measures how quickly growth rises t = time, number of days The data (collected by the Department of Biology at Virginia Tech) are as follows: Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Day 1 1 1 3 3 3 6 6 6 15 15 15 21 21 21 y (Total Protozoa) 17 21 16 30 25 25 33 31 32 34 33 33 39 35 36

(a) Estimate ß\ and ß2 using nonlinear regression. Supply your own starting values.

(b) Give estimated standard errors of the parameter estimates.