Consider the differential equation dp dt = kp1 + c, where k > 0 and c ≥ 0. in section 3.1 we saw that in the case c = 0 the linear differential equation dp/dt = kp is a mathematical model of a population p(t) that exhibits unbounded growth over the infinite time interval [0, ∞), that is, p(t) → ∞ as t → ∞. see example 1 in that section. (a) suppose for c = 0.01 that the nonlinear differential equation dp dt = kp1.01, k > 0, is a mathematical model for a population of small animals, where time t is measured in months. solve the differential equation subject to the initial condition p(0) = 10 and the fact that the animal population has doubled in 8 months. (round the coefficient of t to six decimal places.) p(t) = (b) the differential equation in part (a) is called a doomsday equation because the population p(t) exhibits unbounded growth over a finite time interval (0, t), that is, there is some time t such that p(t) → ∞ as t → t −. find t. (round your answer to the nearest month.) t = months (c) from part (a), what is p(80)? p(160)? (round your answers to the nearest whole number.) p(80) = p(160) = 8 months