Calculating Population Growth Rate using Derivatives

[cdoss]

Homework Statement

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.

Homework Equations

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

 

[eumyang]

P(t)=500(1+(4t/(50+t²), where t is measured in hours.

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).

 

[tiny-tim]

hi cdoss!

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

where is there a product? i only see a quotient

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