(2 points) another model for a growth function for a limited pupulation is given by the gompertz function, which is a solution of the differential equation dpdt=cln(kp)p where c is a constant and k is the carrying capacity. (a) solve this differential equation for c=0.05, k=1000, and initial population p0=100. p(t)= . hint: note that dpdt=cln(kp)p=?c(lnp?lnk)p and then use separation of variables with u-substitution in the integration step (or do this mentally). (b) compute the limiting value of the size of the population. limt?[infinity]p(t)= . (c) at what value of p does p grow fastest? p= . hint: differentiate dpdt again with respect to t (implicitly) and use the first derivative test to find the value of p that gives a maximum in dpdt.
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Category: ecology |
Author: Giiwedin Frigyes

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