Answer is B please show me how to get there Multiple choice

Answer is B, please show me how to get there

Multiple choice questions: only one correct answer for each question. Consider the following source-free transient RLC circuit for t greaterthanorequalto 0. Assume that the voltage v(t) for t greaterthanorequalto 0 is of the form v(t)=A.e^-2t+B.e^-8t V. If the inductor value if 1/2 H, determine the values for the resistor. R=1/20ohm R=8/10ohm R=5ohm R=80ohm You cannot determine R without also knowing C

Solution

APPLY LAPLACE TRANSFORM

V(S)=(A/(S+2))+(B/(S+8))

Charastics eauation is (S+2)(S+8)

S^2+(10S)+16 -------(1)

IN PARALLEL RLC Charastics eauation is S^2+(1/RC)S+(1/LC) ----(2)

COMPARE 1 AND 2

(1/LC)=16

C=(1/16*0.5)

C=0.125F

1/RC=10

R=1/(10*0.125)

0.8 OHM