Question

What rule is this? Number of Hours (N): 1, 2, 3, 4, 5, 6Bacteria Count (X): 2, 4, 8, 16, 32, 64N = 2xN = x + 2N = 2^xN = 2x + 1The number of bacteria N can be calculated from the number of hours x in growth of bacteria.

Answer 1

$N=2^x$

Explanation

Step 1

Let

$\begin{gathered} N\text{ X} \\ 1\rightarrow2 \\ 2\rightarrow4 \\ 3\rightarrow8 \\ 4\rightarrow16 \\ 5\rightarrow32 \\ 6\rightarrow64 \end{gathered}$

now, check the differences

$\begin{gathered} 4-2=2 \\ 8-4=4 \\ 16-8=8 \\ 32-16=16 \\ 64-32=32 \end{gathered}$

the difference are not equal, so we are looking for a geometric rule

Hence

$\begin{gathered} N=2^x \\ \end{gathered}$

I hope this helps you