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Home Q & A Board Biology-Related Homework Help Cell Biology
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leh3188 leh3188
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5 years ago
A bacterial population undergoing exponential growth (g = 0.5 h) wil grow from a size of 10^3 to 10^9 cells in about how many hours?
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Educator
5 years ago
Here's what we know:

Growth rate \((n)\) is \(0.5 / hour\)

Initial population \((a)\) \(10^3=1000\)

Final population \((y)\): \(10^9=1,000,000,000\)

\(y=ae^{nt}\)

\(10^9=1000e^{0.5t}\)

\(\frac{10^9}{1000}=e^{0.5t}\)

\(\ln \left(\frac{10^9}{1000}\right)=0.5t\)

\(\frac{\ln \left(\frac{10^9}{1000}\right)}{0.5}=t\)

\(\therefore t=27.6\) hours to reach \(10^9\) cells
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