C4 help please!

OK, I'm struggling on this question (Q21, Ex 4F). I was fine with parts a) and b), but I just can't get my head around c)! help much appreciated!

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

just to make clear

OK, I'm struggling on this question (Q21, Ex 4F). I was fine with parts a) and b), but I just can't get my head around c)! help much appreciated!

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

c. Differentiate, you should have learnt how to differentiate a^x.

Yes, I know how to differentiate a^x, but there are three unknowns? P, Po and t.

Po is a constant, not a variable. Just differentiate it as you would differentiate 2 or 3 or 9999

I get dP/dt=Po(1.09^T)(ln1.09)