Question

While testing a new vaccine, a lab technician noticed that the number of bacteria reduced by half every minute. How long does it take for 3,000 bacteria to reduce to 375? It takes minutes for the number of bacteria to reduce from 3,000 to 375.

Answer 1

The number of bacteria reduces by half every minute - it can be represented by the equation:
$x=x_0 \times (\frac{1}{2})^n$
where x₀ is the initial number of bacteria and x is the number of bacteria after n minutes.

$x_0=3000 \\ x=375 \\ \\ 375=3000 \times (\frac{1}{2})^n \\ \frac{375}{3000}=(\frac{1}{2})^n \\ \frac{1}{8}=(\frac{1}{2})^n \\ (\frac{1}{2})^3=(\frac{1}{2})^n \\ n=3$

It takes 3 minutes for the number of bacteria to reduce from 3000 to 375.