The rate of bacteria growth in a laboratory experiment was at 16% per hour. If this experiment is repeated and

Question

begins with 5 grams of bacteria, how much bacteria should be expected after 12 hours? Round to the nearest
tenth of a gram.

Answer 1

db/dt = .16 b

db/b = .16 dt

ln b = .16 t + c

e^ln b = b = e^(.16 t +c) = C e^.16 t

or more simply
b = C e^.16 t
when t =0 , e^.16 t = 1
so
C = value when t = 0
b = 5 e^(.16*12)
b = 34.1 grams