Consider the differential equationdpdt= kp1 + c, wherek > 0andc ≥ 0.in section 3.1 we saw that in the casec = 0the linear differential equationdp/dt = kpis a mathematical model of a population p(t) that exhibits unbounded growth over the infinite time interval[0, [infinity]),that is, p(t) → [infinity]ast → [infinity].see example 1 in that section.(a) suppose forc = 0.01that the nonlinear differential equationdpdt= 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 conditionp(0) = 10and the fact that the animal population has doubled in 6 months. (round the coefficient of t to six decimal places.)p(t) =) 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 thatp(t) → [infinity]ast → t −.find t. (round your answer to the nearest month.)t =(c) from part (a), what is p(50)? p(100)? (round your answers to the nearest whole number.)p(50) = (100)=