Register to reply

Bacteria Growth Problem.

by QuantumTheory
Tags: bacteria, growth
Share this thread:
May11-05, 12:22 AM
P: 224
My friend had to do this problem in Calculus BC. I'm no good at calculus, but I decided it was be fun for someone to figure it out for me.

A bacteria culture starts with 500 bacteria and grows at a rate proportional to its size. After 3 hours there are 8000 bacteria.
(a) Find an expression for the number of bacteria after t hours.
(b) Find the number of bacteria after 4 hours.
(c) Find the rate of growth after 4 hours.
(d) When will the population reach 30,000?

I think it involves differential equations.
Phys.Org News Partner Science news on
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
May11-05, 01:28 AM
P: 321
Quote Quote by QuantumTheory
but I decided it was be fun for someone to figure it out for me.

Start with [tex]y=Ae^{kt}[/tex]
May11-05, 05:31 AM
P: 21
Yeah that amused me too .I'd probably start a little earlier:

Growth proportional to size implies.....


with the intial condition [tex]y(0)=500[/tex] and the time t = 3 (in hours!) condition [tex]y(3)=8000[/tex].

Your mission, should you choose to accept it, is to find the general solution to the DE above, and the values of k and the constant of integration A.

That's the model, the rest should be ok?

Register to reply

Related Discussions
Growth of bacteria.. diff. eq... help Calculus & Beyond Homework 3
Bacteria growth rate Differential Equations 4
Growth problem Calculus & Beyond Homework 11
Growth Problem Calculus & Beyond Homework 3
Population Growth problem Biology 1