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.

An insect population grows exponentially.

(a) If the population triples in 20 days, and 50 insects are present initially, write an exponential function of the form P(t) = P₀ · 3^t/n that models the population.

(b) What will the population be in 47 days?

(c) When will the population reach 700?

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