Problema Solution
If a bacteria population starts with 120 bacteria and doubles every four hours, then the number of bacteria after t hours is n = f(t) = 120 · 2t/4.
Find the inverse of this function.
f −1(n) =
Answer provided by our tutors
What we have to do is convert n = 100*2^(t/3) into a form where
t = "some function of n"
we start with
n = 100*2^(t/3) divide both sides by 100
n/100 = 2^(t/3) now take the log of both sides
log(n/100) = log(2^(t/3)) using the laws of logarithms this is the same as
log(n/100) = (t/3) log(2) multiply both sides by 3
3log(n/100) = t log(2) and divide both sides by log(2)
3log(n/100)/log(2) = t
t = 3log(n/100)/log(2)
the inverse function is f^(-1)(n) = 3log(n/100)/log(2).