5. Find the inverse Laplace transform of the function F(s). e -2s (a) F(s) = s2+4 (s-2)e-s (b) F(s) = $2-4s+3 6. Use Laplace transform to find the solution of the initial value n

Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.

F(s) Use (8), f(t) dt = L-1,{S\, to evaluate the given inverse transform. (Write your answer as a function of t.) 1 15(s – 1) .