Problems 29 and 30 use the following discussion: Uninhibited growth can be modeled by exponential functions other than A(t) = A₀e^kt. For example, if an initial population P₀ requires n units of time to double, then the function P (t) = P₀ · 2^t/n models the size of the population at time t. Likewise, a population requiring n units of time to triple can be modeled by P (t) =  P₀ · 3^t/n. The population of a town is growing exponentially.

(a) If its population doubled in size over an 8-year period and the current population is 25,000, write an exponential function of the form P(t) = P₀ · 2^t/n that models the population.

(b) What will the population be in 3 years?

(c) When will the population reach 80,000?

(d) Express the model from part (a) in the form A(t) = A₀e^kt.