Question

If a bacteria population starts with 80 bacteria and doubles every four hours, then the number of bacteria after t hours is n = f(t) = 80 · 2t/4. (a) Find the inverse of this function.

Answer 1

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

= $n=f(t) = 80*2^{\frac{t}{4} }$

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.

$ln n =ln80+\frac{t}{4} ln 2\\\frac{t}{4} =\frac{ln\frac{n}{80} }{ln 2} \\t = 4\frac{ln\frac{n}{80} }{ln 2}$

this is the inverse function.