Question

Wilbur is working in a lab testing bacteria populations. After starting out with a population of 323 bacteria, he observes the change in population and notices that the population doubles every 29 minutes.Step 2 of 2 : Find the population after 1 hour. Round to the nearest bacterium.

Answer 1

We will have the following:

First, we know that every 29 minutes it will double, so "29" will be our base unit.

Now, knowing it doubles each time unit we use this to determine the rate:

$646=323(1+r)^1\Rightarrow2=1+r\Rightarrow r=1$

Now, we since we have that 29 minutes is our base unit, we determine the equivalet for the 1 hour (60 minutes):

$x=\frac{60\min\cdot1}{29\min}\Rightarrow x=\frac{60}{29}$

Now, we determine the population after that time:

$f(\frac{60}{29})=323(2)^{(60/29)}\Rightarrow f(\frac{60}{29})=1355.261818\ldots$$\Rightarrow f(60/29)\approx1355$

So, the population after 1 hour is approximatelly 1355.