85 gram kitten differential equation

Question

A kitten weighs 85 grams at birth. During the first four weeks after the kitten's birth, it's weight in grams is given by the function W that satisfies the differential equation dW/dt=kW, where t is measured in days and k is some positive constant. Which of the following could be an expression for W(t)?

Answer 1

We separate variables: dW/dt = kW; dW/W = kdt; ∫dW/W = k∫dt, lnW = kt + lnC; W = Ce^kt; t = 0 W = 85 g

C = 85g and W(t) = 85e^kt.