Problem 14.3-4

We want F(s) = L[A*(1 – e ^{- bt}u(t)] = A* L (u(t) – e ^{- bt}u(t))

F(s) = A*[ L(u(t)) – L(u(t)*e ^{- bt})] because the Laplace transform is linear.

We know that L[u(t)] = 1/s

And L[u(t)*e ^{– bt}] = 1/(s+b)

Thus we get F(s) = A*(1/s – 1/(s+b))

Which is: