Population growth

smithcity

Hi all, I'm studying for a repeat exam and there's a question here that has me stumped.
I'm not going to ask you to solve it for me, but if you could point me in the right direction it would be appreciated.

At a time t = 0 a population of 1000 bacteria is introduced into a nutrient medium. At time t the size of the population is given by:

p = 9000(4 + t)

4(9 + t^2)

where time is t measured in hours. Find the maximum size of the population.

Any and all help would be greatly appreciated.

Find [latex]\displaystyle\frac{dP}{dt}[/latex], and let it equal to 0. What do you know about letting a differentiated function equal 0?

smithcity

I'm dimly aware that I need to differentiate the equation, let it = 0, an find two values for t. Determine which is min, and which is max. Then substitute it for t in the equation.

Is that the right track?

Just not too sure about how to differentiate this function
should I be using the :
dy = u.dv + v.du
dx dx dx
method?

smithcity

smithcity wrote: »

I'm dimly aware that I need to differentiate the equation, let it = 0, an find two values for t. Determine which is min, and which is max. Then substitute it for t in the equation.

Is that the right track?

That's exactly right.

Just not too sure about how to differentiate this function
should I be using the :
dy = u.dv + v.du
dx dx dx

method?

That's the product rule.

Since the function is a fraction (quotient), you've to use the quotient rule. The notation in that wiki article is the hardest part to understand, really.

smithcity

Yup sorry, was just coming back in to edit my mistake when you posted.

Ok, thanks for the help. I'll give it a lash like that.