Chapter 4.1, Problem 64STP

To determine

Determine which expression represents the number of cells after one -half hour.

Answer to Problem 64STP

Th required answer is $2^{10}$

Explanation of Solution

Given information: Given table, $\begin{array}{cc}\begin{array}{l}\text{Time}\\ \left(\min \right)\end{array}& \begin{array}{l}\text{Number}\\ \text{of bacteria}\end{array}\\ 3& 2^1\\ 6& 2^2\\ 9& 2^3\\ 12& 2^4\end{array}$

Calculation:

Let’s rewrite the table:

  $\begin{array}{cc}\begin{array}{l}\text{Time}\\ \left(\min \right)\end{array}& \begin{array}{l}\text{Number}\\ \text{of bacteria}\end{array}\\ 3\cdot 1& 2^1\\ 3\cdot 2& 2^2\\ 3\cdot 3& 2^3\\ 3\cdot 4& 2^4\end{array}$

One -half hour is $30$ minutes, or $3-10$ minutes.

There will be $2^{10}$ bacteria at that time.

Thus the required answer is $2^{10}$

Correct option is A.