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Question

a) The rate of growth of a certain animal population (i.e. the time

derivative / ) is proportional to the number of animals in this population, N. The growth rate, i.e. the coefficient in the proportion mentioned above, is described by a constant which has units [1/ ]. Every year a constant number of animals, a, are killed.


Write down a differential equation for N and find its general solution. Assume that time t has units [years].


b) Consider a population with initial size 0= ( =0)=105 and the growth rate =0.011/ . Every year 500 animals are killed. Using your solution calculate the number of animals in the population for =5 .


Instruction:
1. Formulate initial condition.
2. Using the initial condition and the general solution obtained in part a), find the constant of integration and so obtain IVP solution.
3. Use IVP solution to find ( =5).

Step-by-step answer

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