Question

how to solve this question?DE

The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at any time. After 3 hours it is observed that there are 400 bacteria present After 10 hours there are 2000 bacteria present. What is the initial number of bacteria?
(ans: P(0) = 201)

Answer 1

so the DE is:
\(\large y' = ky \) with y(3)=400 and y(10)=2000

solving that differential equation you'll get:
\(\huge y(t)=Ce^{k\cdot t} \)
where t is in hours.
using those given values, you'll need to find C and k....
this implies solving a system of equations. can you tell me those two equations?

Answer 2

ok.... i'll give you one of 'em:
\(\huge 400=Ce^{3\cdot k} \)
give me the other one...

Answer 3

\[2000 = Ce ^{10t}\]

thanks!