A bacteria culture started with a number of bacteria and grows at a rate proportional to the number of bacteria.

a) If y (t) is the number of bacteria at time t measured in hours, give a differential equation that describes the behavior of y (t) . Your answer will include a constant k representing the relation of proportionality, as well as the variable y.

y'=

b) Solve the differential equation above to find the number of bacteria as a function of time t . Your solution will depend on k and the initial number B bacteria.

y (t) =

c) Given that after 2 hours the number of bacteria has quintupled, find the exact value of k .

k =

d) In the case of (c), what can be said about the following ratios: