Bacterial Growth: Solving an ODE for Population Size

[S.N.]

Homework Statement

A cell of some bacteria divides into two cells every 40 minutes. The initial population is 2 bacteria.

a)Find the size of the population after t hours
b) Find the size of the population after 6 hours.
c) When will the population reach 12?

Homework Equations

None given.

The Attempt at a Solution

taking t = time in hours, y(t) = population,

we say that

dy/dt = (3/2)y --- the 3/2 converts from hours to the 40 min growth period
dy/y = (3/2)dt
integrate...
ln(y) = (3/2)t + C --- C is arbitrary constant
y = [e^( (3/2)t )] * L -- L is arbitrary constant analogous to e^C.

we know that y(0) = 2, so to solve initial value problem,

2 = 1*L

therefore L = 2

and the solution for part a) should be y(t) = 2 e^[(3/2)t]

but this solution is unfortunately incorrect and I don't see how to fix it. Of course it holds for y(0) as it should, but it falls apart when I check other values. a friend mentioned something about "adding or subtracting a 1" somewhere but I don't see where I would do that, and even if I did I wouldn't understand the justification.

Any help is appreciated, thanks!

 

[Kizaru]

Look at your ODE. It's missing something. The population _DOUBLES_ every 40 minutes. You seem to have forgotten about this fact.

A suggestion: convert to hours at the very end.