# Population Growth Differential Equations

1. Feb 12, 2012

### MathWarrior

1. The problem statement, all variables and given/known data
A biologist prepares a culture. After 1 day of growth the biologist counts 1000 cells. After 2 days he counts 3000. Assuming a Malthusian model what is the reproduction rate and how many cells were present initially.

2. Relevant equations

$P(t) = Ce^{rt}$

3. The attempt at a solution
$P(1) = P(0)e^{r}$
$1000 = P(0)e^{r}$

$P(2) = P(0)e^{r2}$
$3000 = P(0)e^{r2}$

Not sure how I am suppose to get the rate here.... or even start really..

2. Feb 12, 2012

### vela

Staff Emeritus
That's a good start. It's all algebra now. Try solving for P(0) in both equations and then set them equal to each other.

3. Feb 12, 2012

### Ray Vickson

Maybe your notation is making it hard for you to see what is happening. If you set c = P(0) and x = exp(r), you have c*x= 1000 and c*x^2 = 3000. Surely you can get c and x from these!

RGV