1. ## Growth Formula

A colony of 10 000 roughly circular organisms grows in culture, each with density 0.4 g/cm2 and radius r cm. The energy consumption of the colony is given by

E = 250*[ m / (1000+m) ]

m is its total mass. Find E as a function of the radius r, and determine what

I know that mass = density*radius, so

E = 250[ (0.4*pi*r^2) / (1000 + 0.4*pi*r^2) ]

What happens to E as r gets larger?

2. ## Re: Growth Formula

Originally Posted by Manni
A colony of 10 000 roughly circular organisms grows in culture, each with density 0.4 g/cm2 and radius r cm. The energy consumption of the colony is given by

E = 250*[ m / (1000+m) ]

m is its total mass. Find E as a function of the radius r, and determine what

I know that mass = density*radius, so

E = 250[ (0.4*pi*r^2) / (1000 + 0.4*pi*r^2) ]

What happens to E as r gets larger?
Judging by your units: mass = density * area [although you did do the correct calculation].

Are you allowed to use L'hopital's rule?

Essentially you want to find $\displaystyle \lim_{r \to \infty} E(r)$

3. ## Re: Growth Formula

What is L'hopital's rule? And how would I evaluate this limit? It seems a little tricky