Suppose a gas consists of molecules of type A. When the gas is heated a second substance B is formed by molecular collision. Let A(t) and B(t) denote, in turn, the number of molecules of types A and B present at time t ≥ 0. A mathematical model for the rate at which the number of molecules of type A decreases is

dA/dt = -kA², k > 0.

(a) Determine A(t) if A(0) = A₀.

(b) Determine the number of molecules of substance B present at time t if it is assumed that A(t) + B(t) = A₀.

(c) By hand, sketch rough graphs of A(t) and B(t) for t ≥ 0.