7 02 points I Previous Answers StitzCA3 87016 36 Submissions

7. 0/2 points I Previous Answers StitzCA3 8.7.016. 3/6 Submissions Used My Notes Ask Your If a population increases according to The Law of Uninhibited Growth, the number of organisms N at time t is given by the formula N(t) = Noekt, No (read \"N nought\') is the initial number of organisms and k > 0 is the constant of proportionality which satisfies the where N 0) equation (instantaneous rate of change of N(t) at time t) kN(). A certain bacteria culture follows the Law of Uninhibited Growt are 19,000 bacteria. How many bacteria were present initially? (Round your answer to the nearest N(0)= h. After 10 minutes, there are 15,000 bacteria. Five minutes later, there | bacteria How long before there are 50,000 bacteria? (Round your answer to two decimal places.) min Additional Materials Reading Submit Answer Save Progress My Notes Ask Your T al-/1 points StitzCA3 8.7.017. 0/6 Submissions Used Consider the system of nonlinear equations below. 4,2 x y

Solution

15000 = N_oe^10k (1)

19000 = N_oe^15k (2)

==>> e^5k = 19000/15000 ===> k = 0.047277756 min^-1

putting in (1), we have

15000 = N_oe^{10(0.047277756)}

=> N_o = 9349

b) 50000 = 9349e^0.047277756t

==> t = 35.465946 min