Question

The number of bacteria in a culture is modeled by the function
n(t) = 600e^0.5t
where t is measured in hours.
(a) What is the initial number of bacteria?
(b) What is the relative rate of growth of this bacterium population? Express your answer as a percentage.
(c) How many bacteria are in the culture after 3 hours? (Round your answer to the nearest whole number.)
(d) After how many hours will the number of bacteria reach 40,000? (Round your answer to two decimal places.)

Answer 1

a) fot the initial number of bacteria u must think at hour zero
n(t) = 600e^0.5(0)=600

b) for the rate of change u must think in a derivative

dn/dt=300e^0.5t

c)
n(t) = 600e^0.5(3)=2689

d) Solve an equation 40000=600e^0.5t
66.67=e^0.5t

ln(66.67)=0.5t
t=8.4 == 8 hours

b) im not sure because the change is not linear im not sure you cant express on percentage