Question

Convert the given exponential function to the form indicated. Round all coefficients to four significant digits. HINT [See Example 4 "Before we go on."] f(t) = 18(0.887)t;  f(t) = Q0e−kt

Answer 1

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)