Chapter 6.3, Problem 45E

Weight Gain A calf that weighs 60 pounds at birth gains weight at the rate $dw/dt=k\left(1200-w\right)$, where w is the weight in pounds and t is the time in years.

(a) Find the general solution of the differential equation.

(b) Use a graphing utility to graph the particular solutions for $k=0.8,0.9,\text{and}1$.

(c) The animal is sold when its weight reaches 800 pounds. Find the time of sale for each of the models in part (b).

(d) What is the maximum weight of the animal for each of the models in part (b)?