SOLUTION: convert the given exponential function to the form indicated. Round all coefficients to four significant digits. f(t) = 11(0.957)^t; f(t) = Q0^e−kt

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: convert the given exponential function to the form indicated. Round all coefficients to four significant digits. f(t) = 11(0.957)^t; f(t) = Q0^e−kt      Log On


   

Question 1204505: convert the given exponential function to the form indicated. Round all coefficients to four significant digits.
f(t) = 11(0.957)^t; f(t) = Q0^e−kt
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

There's a typo.
The Q0^e-kt should be Q0*e^(-kt)

Compare f(t) = 11(0.957)^t with f(t) = Q0*e^(-kt) to find that Q0 = 11.

The e^(-kt) part is the same as (e^(-k))^t or (1/(e^k))^t

Set e^(-k) equal to 0.957 to determine k.
e^(-k) = 0.957
Ln( e^(-k) ) = Ln(0.957)
-k*Ln( e ) = Ln(0.957)
-k*1 = Ln(0.957)
-k = Ln(0.957)
k = -1*Ln(0.957)
k = 0.043952 approximately
k = 0.0440 when rounding to 4 significant digits.

Answer:
f(t) = 11*e^(-0.0440t)