# Growth Formula

• Oct 17th 2011, 11:28 AM
Manni
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?
• Oct 17th 2011, 11:40 AM
e^(i*pi)
Re: Growth Formula
Quote:

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 $\lim_{r \to \infty} E(r)$
• Oct 17th 2011, 11:45 AM
Manni
Re: Growth Formula
What is L'hopital's rule? And how would I evaluate this limit? It seems a little tricky