A population of bacteria is changing at a rate of dp/dt = (3000/e^3+3t) , where t is the time in minutes. If the initial population is 13000, find the population when t=5 minutes.
so i have to use substitution on this...i tried let u = 3t, but the problem didnt work out right on the quiz and he corrected it saying it should have been u = e^3 + 3t, which differentiates into du=3dt => (1/3)du=dt ? what happened to the e^3? doesnt e^3 = e^3 after you differentiate it?