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?

1 Answer
Jacobi J.
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 #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!

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