Under optimal conditions, the growth of a certain strain of E. Coli is modeled by the Law of Uninhibited Growth N(t)=N0ekt where N0 is the initial number of bacteria and t is the elapsed time, measured in minutes. From numerous experiments, it has been determined that the doubling time of this organism is 4 minutes. Suppose 1500 bacteria are present initially.

(a) Find the growth constant k. Round your answer to four decimal places.

k=

Tries 0/99

(b) Find a function which gives the number of bacteria N(t) after t minutes.

N(t)=

Tries 0/99

(c) How long until there are 20000 bacteria? Round your answer to the nearest minute.

t=

minutes