Answer:
Step-by-step explanation:
given that a bacteria population starts with 80 bacteria and doubles every four hours,
The function representing the number of bacteria after t hours
= [tex]n=f(t) = 80*2^{\frac{t}{4} }[/tex]
We are to find the inverse of the function
i.e. we must make t = g(n) where g is a function of n.
Take log on both sides.
[tex]ln n =ln80+\frac{t}{4} ln 2\\\frac{t}{4} =\frac{ln\frac{n}{80} }{ln 2} \\t = 4\frac{ln\frac{n}{80} }{ln 2}[/tex]
this is the inverse function.
