Consider a population of bacteria that grows according to the initial value problem dp/dt=p/10, p(0)=300. find the population size after 40 hours

 dP / dt = P / 10
 We apply separable variables:
 dP / P = dt / 10
 We integrate both sides:
 Ln (P) = t / 10 + C
 We rewrite the equation:
 Exp (Ln (P)) = Exp (t / 10 + C)
 P = Exp (C) * Exp (t / 10)
 P = C * Exp (t / 10)
 We look for the constant using:
 P (0) = 300
 300 = C * Exp (0/10)
 300 = C * 1
 C = 300
 We rewrite the equation:
 P = 300 * Exp (t / 10)
 After 40 hours we have:
 P = 300 * Exp (40/10)
 P = 16379.44501
 
 the population size after 40 hours is: 
 P = 16379

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