sin , pulation on campus is given by dit-034-P)(P-1). 6. Suppose a model for the roadrunner population on campussvn by0.3(4P) P(t) if the initial population is Use the first and second derivative...
Suppose that the rate of change of a population is given by: dP dt = kP(M-P) a) What model of population growth is this ? b) What does it predict for the growth of the population as the population increases ? c) Sketch what happens to the population if the initial population, Po, were such that G) 0< Po< M/2, (ii) M/2 < PoM and (iii) Po > M (all on the same graph of population as a function of...
1. (Model with a threshold level) Suppose that a given population can keep increasing just if the initial size is large enough and it dies out otherwise. The level that allows the increase of population is called a threshold level. In this case the rate of increase is proportional to the population size P and the difference of the present population size and the threshold level T (see class notes). Write the corresponding mathematical model for this case a Let...
Problem #6: A model for a certain population P(1) is given by the initial value problem dP-H10-3-10-13 P), dt P(0)= 100000000, where t is measured in months (a) What is the limiting value of the population'? (b) At what time (i.e., after how many months) will the populaton be equal to one half of the limiting value in (a)? Do not round any numbers for this part. You work should be all symbolic.) Problem #6(a): 10000000000 Enter your answer symbolically,...