Question

The population of a bacteria culture doubles in number every 12 minutes. The ratio of the number of bacteria at the end of 1 hour to the number of bacteria at the beginning of that hour is

• A. $8:1$
• B. $16:1$
• C. $32:1$
• D. $60:1$

Answer 1

The correct option is C $32:1$

If a number is multiplies repeatedly by 2 for n times then the last result will be $2^n\times number$.

Let the number of bacteria is $a$. The number of bacteria doubles every $12$ minutes, which means that it doubles $5$ times in an hour.
Therefore,
$\left(2\right)\left(2\right)\left(2\right)\left(2\right)\left(2\right)a=a\times 2^5$
$=32a$ at the end of the hour.
Thus, the ratio of the number of bacteria at the end of 1 hour to the number of bacteria at the beginning of that hour is $\frac{32a}{a}=32:1$.