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?

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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?

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Answer 1 · 2018-07-03T03:56:10

$2^{x}$ $2^x$

Explanation:

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

How do we get from $x = 1$ $color(blue)(x=1)$ to $y = 2$ $y=2$ ? We can multiply it by two or raise $2$ $2$ to the $1$ $color(blue)(1)$ st power.

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

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

Therefore, our expression is

$2^{x}$ $2^x$

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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?

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