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 ≥ 0 where P is regarded as a continuous function of t and P₀ is the 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 significant figures.

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