# Thread: Rate of change. Forming an equation

1. ## Rate of change. Forming an equation

A forest is buring so that, $\displaystyle t$ hours after the start of the fire, the area is $\displaystyle A$ hectares. It is given that, at any instant, thhe rate at which the area is increasing is proportional to $\displaystyle A^2$.

i) Write down a differential equation which models this situation.

$\displaystyle \frac{dt}{dA}= A^2$ ?

ii)After 1 hour, 1000 hetares have been burnt; after 2 hours, 2000 hectares have been burnt. Find after how many hours 3000 hectares have been burnt.

Am i right for part i)?
Not sure how to do part ii)

2. Originally Posted by George321
A forest is buring so that, $\displaystyle t$ hours after the start of the fire, the area is $\displaystyle A$ hectares. It is given that, at any instant, thhe rate at which the area is increasing is proportional to $\displaystyle A^2$.

i) Write down a differential equation which models this situation.

$\displaystyle \frac{dt}{dA}= A^2$ ?

ii)After 1 hour, 1000 hetares have been burnt; after 2 hours, 2000 hectares have been burnt. Find after how many hours 3000 hectares have been burnt.

Am i right for part i)?
Not sure how to do part ii)
It is given that, at any instant, thhe rate at which the area is increasing is proportional to $\displaystyle A^2$.
So $\displaystyle \frac{dA}{dt} \propto A^2 \Rightarrow \frac{dA}{dt} = k A^2$ where k is a constant.