The Student Room Group

C4 Differential equ. Mixed ex. 4F

Completely tearing my hair out on this one...
It's in the book (Q21) but here it is anyway:

A population P is growing at the rate of 9% each year and at time t years may be approximated by the formula

P=P0 (1.09)t , t>(or equal to) 0

where P is regarded as a continuous function of t and P0 is the starting population at time t=0.

(a) Find an expression for t in terms of P and P0.

(b) Find the time T years when the population has doubled from its value at t=0, giving your answer to 3 s. f.

(c) Find, as a multiple of P0, the rate of change of population dP/dt at time t=T


Okay I've done (a) and (b) but it's (c) I really don't know how to do. :mad: :mad: ... any help will be greatly appreciated lol
Reply 1
c) lnP = ln(P0) + t.ln(1.09)

(1/P)(dP/dt) = ln(1.09)
dP/dt = P.ln(1.09) = [P0ln(1.09)](1.09)t

And now sub in your value of t at time T...