Question

The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 4000.
(a) Find a function
n(t) = n0ert
that models the population after t hours.
n(t) =

b)Find the population after 1.5 hours. (Round your answer to the nearest whole number.)
n(1.5) = bacteria

Answer 1

n = 1000 e^(kt)

note when t = 0, e^kt = e^0 = 1
so 1000*1 at t =0

4000/1000 = 4 = e^(k*1)
or
e^k = 4
k = ln 4 = 1.386
so
n = 1000 e^ (1.386 t)
it t = 1.5
n = 1000 e^(2.079)
n = 8000