A species of bacteria doubles in population every 6.5 hours. There were 100 bacteria to start with. What is the hourly growth rate of the bacteria? How many bacteria will there be after a day and a half?
I know that every 6.5 hours is 1 time interval. So, the equation for the bacteria is y=100(2)+^x.
My biggest question to how to find the hourly growth rate. I thought that if the bacteria doubles (increases by 100%) every 6.5, then the bacteria increases by k% every hour. I thought I could just divide by 100 by 6.5 to get k.
Once I have that, then I finish the problem. Am I correct so far?
If $x$ is the number of hours that has elapsed since this experiment began, then the number of bacteria is $100(2)^{\frac{x}{6.5}}$.
Now that we have this formula, the simplest way to determine the hourly growth rate is to simply plug $1$ in for $x$ and we see that:
$100(2)^{\frac{1}{6.5}}=111.25$
$111.25-100=11.25$, so the hourly growth rate is $11.25$%.