Question: The population of a bed of clams in the Great South Bay of Long Island is described by the logistic function with k=0.0001 and t in years. Assume that there are 400 clams initially and that the maximum population size is 5200.
a) Find the growth function G(t) for the clams.
b) Find the population and rate of growth of the population after the following times of 1 year and 4 years.
Here is my solution:
a) G (t)=5200/(1+12e^-0.52t) (the growth function)
b) For 1 year population is G (t)= 5200/8.13425=639 and growth rate 1/1 ln 639/400=0.1(1.59750)=59.750
For 4 year population is G (t) = 5200/2.49916=2081 and growth rate ¼ in 2081/400= 0.25 (1.64914)=41.228
I left some of the steps out, and I am not so sure I have the problem set up rate, any help would be appreciated. Thanks.
Jen
a) Find the growth function G(t) for the clams.
b) Find the population and rate of growth of the population after the following times of 1 year and 4 years.
Here is my solution:
a) G (t)=5200/(1+12e^-0.52t) (the growth function)
b) For 1 year population is G (t)= 5200/8.13425=639 and growth rate 1/1 ln 639/400=0.1(1.59750)=59.750
For 4 year population is G (t) = 5200/2.49916=2081 and growth rate ¼ in 2081/400= 0.25 (1.64914)=41.228
I left some of the steps out, and I am not so sure I have the problem set up rate, any help would be appreciated. Thanks.
Jen
