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Hi I Am Trying Solve Part C Can You Help Me Thank You We Are Learning Differenti

Exploding population (10 points). Records of the world’s human population, it has been claimed, in-dicate that the growth rate of the population is not constant, but rather proportional to the populationsize itself. This means that the rate of growth is kp(t), where p(t) denotes the world population (num-ber of living humans) at year t, and k: is a constant. Population records suggest that k z 4.1 x 10—12.The differential equation describing this model is dp_ _ 2a—(kpM—kp- (a) Find the general solution to this equation. (b) Find the particular solution that also satisfies the condition that the current population is M2018) =7.6 x 109. Ic) Show that there is a time when the population will become infinite. At which year will thepepulation explosion happen according to this model?

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