We use P = i•e^rt for exponential population growth, where P = end population, i = initial population, r = rate, and t = time P = 2•i = 2•15 = 30, so 30 = 15 [e^(r•1)], or 30/15 = 2 = e^(r) ln 2 = ln (e^r) .693 = r•(ln e), ln e = 1, so r = .693 Now that we have our doubling rate of .693, we can use that r and our t as the 12th hour is t=11, because there are 11 more hours at the end of that first hour So our initial population is again 15, and P = i•e^rt P = 15•e^(.693×11) = 15•e^(7.624) P = 15•2046.94 = 30,704
