Question

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?

Answer 1

`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 `color(blue)(x=1)` to `y=2`? We can multiply it by two or raise `2` to the `color(blue)(1)`st power.

How about from `color(blue)(x=2)` to `y=4`? Once again, we can multiply `x` by two or raise `2` to the `color(blue)(2)`nd power.

How about from `color(blue)(x=5)` to `y=32`? This time, we can't multiply `x` by two, but we can raise `2` to the `color(blue)(5)`th power to get `y=32`.

Therefore, our expression is

`2^x`

Hope this helps!