69. For Example 5.21, let M(t) = E[D(t)]

(a) Argue that M(t + h) = M(t) + e−αtM(h)

(b) Argue that M(t + h) = M(h) + e−αhM(t)

(c) Argue that M(h) = λhμ + o(h)

(d) Use parts

(a) and

(c) to derive and then solve a differential equation for M(t).

(e) Use parts

(b) and

(c) to derive and then solve a differential equation for M(t).