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

Dottie Parra 2021-09-21 Answered
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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Expert Answer

izboknil3
Answered 2021-09-22 Author has 16149 answers
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
\(\displaystyle{5.0123}={x}-{3}\)
Add both sides 3.
\(\displaystyle{8.0123}={x}\)
Conclusion:
Approximately after 8 hours, the bacteria culture became 200,000.
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