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?
Each hour the number of bacteria will double.
Let $\displaystyle B_i$ represent the number of bacteria at hour $\displaystyle i$. If there are $\displaystyle n$ bacteria to begin with...
Then
$\displaystyle B_0 = n$
$\displaystyle B_1 = 2n$
$\displaystyle B_2 = 4n = 2^2n$
$\displaystyle B_3 = 8n = 2^3n$
$\displaystyle B_4 = 16n = 2^4n$.
So what do you think $\displaystyle B_x$ is?
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.