The number of bacteria after t hours is given by n(t)=250 e^0.15t a) find the initial number of bacteria and the rate of growth or decay. b) find the number of bacteria after 2 days c) how many hours will it take for the number of bacteria to reach 4000? d) how long will it take for the number of bacteria to triple?

a)

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies . And . The process is:

b) After 2 days means . So, we just replace and operate:

c)

d)