# How do you write an algebraic expression for an experiment where in 1 hour there were 2 bacteria, 2 hours there were 4 bacteria, and in 5 hours there were 32 bacteria?

Jul 3, 2018

${2}^{x}$

#### Explanation:

Let's define $x$ as being equal to hours, and $y$ as being equal to the number of bacteria.

How do we get from $\textcolor{b l u e}{x = 1}$ to $y = 2$? We can multiply it by two or raise $2$ to the $\textcolor{b l u e}{1}$st power.

How about from $\textcolor{b l u e}{x = 2}$ to $y = 4$? Once again, we can multiply $x$ by two or raise $2$ to the $\textcolor{b l u e}{2}$nd power.

How about from $\textcolor{b l u e}{x = 5}$ to $y = 32$? This time, we can't multiply $x$ by two, but we can raise $2$ to the $\textcolor{b l u e}{5}$th power to get $y = 32$.

Therefore, our expression is

${2}^{x}$

Hope this helps!