[tex]\sqrt[5]{2}-1 = 1 +x - 1[/tex]Answer:
14.87% per hour
Step-by-step explanation:
Let's pretend we're starting with one bacteria.
Double of one is two
We're gonna have to use this formula: A = P(1 + x)ⁿ
A = Amount (which is 2)
P = Initial amount (which is 1)
x = percentage per time (hour)
n = amount of time (hours)
So our equation will look like this:
2 = 1(1 + x)⁵
First, we need to root both sides to isolate (1 + x)
[tex]\sqrt[5]{2} = \sqrt[5]{(1+x)}[/tex]
[tex]\sqrt[5]{2} = 1 +x[/tex]
Then subtract both sides by 1
[tex]\sqrt[5]{2}-1 = 1 +x - 1[/tex]
[tex]x=\sqrt[5]{2}-1[/tex]
[tex]\sqrt[5]{2} = 1.148698355[/tex]
1.148698355 - 1 = 0.148698355
x = 0.148698355
