# Thread: Find Bacteria After x Hours

1. ## Find Bacteria After x Hours

If bacteria double in number every hour, how many bacteria will there be after x hours? Start with 1 bacteria?

MY WORK:

Let B = bacteria

Is the equation B = 2^(x) + 1?

Is this correct?

2. Each hour the number of bacteria will double.

Let $B_i$ represent the number of bacteria at hour $i$. If there are $n$ bacteria to begin with...

Then

$B_0 = n$

$B_1 = 2n$

$B_2 = 4n = 2^2n$

$B_3 = 8n = 2^3n$

$B_4 = 16n = 2^4n$.

So what do you think $B_x$ is?

3. Originally Posted by fdrhs1984
If bacteria double in number every hour, how many bacteria will there be after x hours? Start with 1 bacteria?

MY WORK:

Let B = bacteria

Is the equation B = 2^(x) + 1?

Is this correct?
Unfortunately, this does not even satify the "initial condition". If you started with 1 bacteria, then you should have B(0)= 1 but 2^0+ 1= 1+ 1= 2, not 0. Perhaps you were making the mistake of thinking that 2^0= 0 and added the "1". Drop the "1" and youare exactly correct.

4. So, is the answer B = 2^(x)?

5. No. It's $2^xn$.

6. Thank you very much. You are great!