Consider the initial value problem:
dp/dt = P^2 - 7P + 10
P(0) = 1
where P represents the population of a species (in thousands), and t represents time (in years).
a. Find the explicit solution of the initial value problem to find P as a function of t.
b. What size does the population approach in the long term? (i. e. find the limit as t ---> [infinity] of P).
c. If you could go backwards in time, what size would the population approach? (i. e. find the limit as t ---> -[infinity] of P)