1.
Let c be a positive number, and let A > 0 represent the initial value of a population.
a) Show that the function p(t) = (A^(-c) - ct)^(-1/c) satisfies the differential equation
p'(t) = (p(t))^(1+c)
b) What happens to p(t) as t > (A^(-c)/c) from the left?
2. Find the Maclaurin series...