# A bacterial culture quadruples in size every hour. You begin observing the numbe

A bacterial culture quadruples in size every hour. You begin observing the number of bacteria 3 hours after the culture is prepared. The amount x of bacteria x hours after the culture is prepared represented by $$\displaystyle{y}={192}{\left({4}'-{3}\right)}$$. When will there be 200.000 bacteria? It fo;;ows the equation $$\displaystyle{y}={192}{\left({4}\right)}^{{{x}-{3}}}$$

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Calculation:
The 200000 represents the value of y. Plug in y as 200000 then solve it for x.
Solve the equation for x.
Divide both sides by 192.
$$\displaystyle{1041.6667}={\left({4}\right)}^{{{x}-{3}}}$$
Now, take log on both sides
$$\displaystyle{\log{{\left({1041.6667}\right)}}}={{\log{{\left({4}\right)}}}^{{{x}-{3}}}}$$
Divide both sides by log 4
$$\displaystyle{5.0123}={x}-{3}$$
$$\displaystyle{8.0123}={x}$$
Conclusion:
Approximately after 8 hours, the bacteria culture became 200,000.