Question 187871
Population formula: *[Tex \LARGE P(t)=2^{\frac{t}{4}}] P - population of cells, t - time in minutes



*[Tex \LARGE 6000000000=2^{\frac{t}{4}}]



*[Tex \LARGE \log_{10}(6000000000)=\log_{10}\left(2^{\frac{t}{4}}\right)]



*[Tex \LARGE \log_{10}(6000000000)=\frac{t}{4}\cdot\log_{10}\left(2\right)]



*[Tex \LARGE \frac{\log_{10}(6000000000)}{\log_{10}\left(2\right)}=\frac{t}{4}]



*[Tex \LARGE \frac{4\cdot\log_{10}(6000000000)}{\log_{10}\left(2\right)}=t]



*[Tex \LARGE t=\frac{4\cdot\log_{10}(6000000000)}{\log_{10}\left(2\right)}]



*[Tex \LARGE t \approx \frac{4\cdot9.7781}{\log_{10}\left(2\right)}]



*[Tex \LARGE t \approx \frac{4\cdot9.778}{0.301}]



*[Tex \LARGE t \approx \frac{39.113}{0.301}]



*[Tex \LARGE t \approx 129.929]



Ans: Takes approximately 129.929 minutes for pop. to reach 6,000,000,000 cells