ocr c4 differential equations question

any help to this question would be much appreciated!!

A forest is burning so that, t hours after the start of the fire, the area burnt is A hectares. It is given that at any instant, the rate at which this area is increasing is proportional to A^2.

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

I got that to be dA/dt = KA^2
Its part (ii) that i cant do....

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

Thanks in advance for any help

Reply 1

al-khwarzimi

integrate

Reply 2

mousy

i know i have to integrate but im having trouble with it

Reply 3

nota bene

Separate variables, so I guess you have INT dt= INT 1/(ka^2) da

Reply 4

al-khwarzimi

dA/dt = kA^2

arrange to get A^-2 dA = k dt

integrate to get (realising that K is constant)

(-1/A) = kt + C (c= integration constant)

then put conditions in (that is t=1 a=1000 and t=2 k= 2000)
to form to silmultaneous equations. Solve them to get k and c values.

then u have an equation of A as a function of t
and put t=3 in that equation to get answer.