You are Here: Home

# Modelling with differential equations question help watch

1. Can anyone help me see where I have gone wrong with this question?

Mould is spreading through a piece of cheese of mass 1 kg in such a way that at a time t days, x kg of the cheese has become mouldy where

dx/dt = 2x(1-x)

Given that initially 0.01 kg of the cheese is mouldy, show that x = (e^2t)/(99+e^2t)

I end up with the solution x = (e^2t)/([1/A] + e^2t), but 1/A evalutes to 100 as 1/0.01 and not 99?

2. (Original post by Dapperblook22)
Can anyone help me see where I have gone wrong with this question?

Mould is spreading through a piece of cheese of mass 1 kg in such a way that at a time t days, x kg of the cheese has become mouldy where

dx/dt = 2x(1-x)

Given that initially 0.01 kg of the cheese is mouldy, show that x = (e^2t)/(99+e^2t)

I end up with the solution x = (e^2t)/([1/A] + e^2t), but 1/A evalutes to 100 as 1/0.01 and not 99?

Rearrange for A or 1/A and plug back in to your expression for x(t)

It might help you if you write your general expression in terms of B=1/A rather than 1/A. You can do this because A is just some arbitrary constant, so rewriting it in terms of some other arbitrary constant doesn't change anything.
3. (Original post by Implication)

Rearrange for A or 1/A and plug back in to your expression for x(t)

It might help you if you write your general expression in terms of B=1/A rather than 1/A. You can do this because A is just some arbitrary constant, so rewriting it in terms of some other arbitrary constant doesn't change anything.
Thank you so much, I see the proof now

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 13, 2016
Today on TSR

### Congratulations to Harry and Meghan!

But did you bother to watch?

### Why are girls so attracted to tall guys?

Poll
Useful resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE