# Rate of Change Derivitive

1. Feb 24, 2012

### cdoss

1. The problem statement, all variables and given/known data
A population of 500 bacteria is introduced into a culture and grows in number according to the equation P(t)=500(1+(4t/(50+t2), where t is measured in hours. Find P'(2), an interpret the results.

2. Relevant equations

3. The attempt at a solution
I used the product rule, sum and difference rule, and the quotient rule, but it seems like I used it a lot and there is a lot of steps that I used. I think I am over-thinking this problem. But I got 10000-200t2/(50+t2)2

2. Feb 24, 2012

### eumyang

Is it supposed to be this?
$$P(t) = 500\left( 1 + \frac{4t}{50 + t^2}\right)$$
I also got something different for P'(t).

3. Feb 24, 2012

### tiny-tim

hi cdoss!
where is there a product? i only see a quotient