[0.8/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 9.4.018. MY NOTES ASK YOUR Let c be a positive number. A differential equation of the form dy = kyl+ c dt where k is a positive constant, is called a doomsday equation because the exponent in the expression ky + is larger than the exponent 1 for natural growth. (a) Determine the solution that satisfies the initial condition y(0) = yo- yo (1 - cyCkt ) (2) (b) Show that there is a finite time t = 7 (doomsday) such that lim y(t) = co. t - T 1 We have y(t) - co as 1 - cykt - 0 , that is, as t - cyk 1 Define T = Then lim y(t) = co. cy k t - T (c) An especially prolific breed of rabbits has the growth term ky.. If 3 such rabbits breed initially and the warren has 21 rabbits after 3 months, when is doomsday (in months)? (Round your answer to two decimal places.) months Need Help? Read It Submit