ANSWER
1319 hours
EXPLANATION
We have that the bacteria colony started with just 2 bacteria.
The colony is growing exponentially. The rate is 10% or 0.01.
The formula for amount of an exponential growth is:
[tex]\begin{gathered} A=a(1+r)^t \\ t\text{ = time in hours} \\ r\text{ = rate = 0.01} \\ a\text{ = intial amount of bacteria = 2} \end{gathered}[/tex]Therefore, we have that:
[tex]\begin{gathered} 1000000=2(1+0.01)^t \\ \frac{1000000}{2}=1.01^t \\ \Rightarrow500000=1.01^t \\ \text{Convert this to logarithm, we have that:} \\ \log _{1.01}50000\text{ = }t \\ \Rightarrow\text{ t = 1318.79 }\cong1319\text{ hours} \end{gathered}[/tex]That is the number of hours it will take to get to 1000000 bacteria.
