Question

If a bacteria population starts with 160 bacteria and doubles every two hours, then the number of bacteria after t hours is n = f(t) = 160 · 2t/2. (a) find the inverse of this function. F −1(n) = explain its meaning.

Answer 1

solution:

$the function should be n=f(t)=160\times 2^{(\frac{t}{4})}\\

n=160\times 2^{(\frac{t}{4})}\\

\frac{n}{160}=2^{\frac{t}{4}}\\

\frac{t}{4}=log^2(\frac{n}{160})log^2\\

t=4log(\frac{n}{160})\\

t=\frac{4log(\frac{n}{160})}{log2}\\

f^{-1}(n)=\frac{4log(\frac{n}{160})}{log2}$