Chapter PS, Problem 4.5P

To determine

To find: The number of bacteria at the beginning of the first day.

Answer to Problem 4.5P

The number of bacteria at the beginning of the first day is $50$ .

Explanation of Solution

Given information:

A bacteria doubles its population every $12\text{h}$ , The number of bacteria after $3$ full days is $1600$ .

Consider the number of bacteria at the beginning of the first day be $x$ .

Increased in the population of the bacteria is given by,

  $P={\left(2\right)}^{n}x$

For three days, the value of $n$ is,

  $\begin{array}{c}n=\frac{24\times 3}{12}\\ =6\end{array}$

The number of bacteria at the beginning of the first day is calculated as,

  $\begin{array}{l}P={\left(2\right)}^{n}x\\ 1600={\left(2\right)}^{6}x\\ x=50\end{array}$

Thus, the number of bacteria at the beginning of the first day is $50$ .