1) Take natural logarithms (Ln) on both sides of the first equation:
f(t) = 18 [0.887]^t => Ln [f(t) ] = Ln (18) + t Ln(0.887)
2) Take natural lograrithms (Ln) on both sides of the second equation:
f(t) = Qo [e] ^ (-kt) => Ln [f(t) ] = Ln(Qo) - kt
3) Make the coefficients equal=>
Ln (Qo) = Ln(18) => Qo = 18
Ln (0.887) = - k => -k = -0.1199
4) Substitute the terms in f(t) = Qo [e]^ (-kt) =>
f(t) = 18 [e]^ ( -0.1199 t)
Answer: 18 [e]^(- 0.1199t)
