During the early years of the zombie apocalypse the Center for Zombie Control fo

Question

During the early years of the zombie apocalypse the Center for Zombie Control found that the number of new zombie cases followed the formula:

Rate of infection = 18:3t^2 thousand zombies per year where t is measured in years after the beginning of zombie apocalypse.

(a) Suppose z is the total number of zombies (measured in thousands of zombies). Express the rate of infection above as a di§erential equation involving z.

(b) Suppose that there are 2 thousand zombies initially. Find a formula for the number of zombies after t years.

Explanation / Answer

Taking as the function r = 18.3t2

a. Derivate the function respect t, we got (18.3*2) t = 36.6t

b. Having a initial population of zombies of 2000, we will have (having the same rate of infection): 2000(18.3t2)

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