Discussion
A rich medium is inoculated with a bacterium that divides every 30 minutes. The number of bacteria at the end of 50 hours is
Answer: D
The number of bacteria is \(1 \times 2^{100}\).
A division every 30 minutes means two generations per hour, so in 50 hours there are \(50 \times 2 = 100\) generations. Starting from one bacterium, the count doubles each generation:
\[ \begin{aligned} N &= N_{0} \times 2^{n} = 1 \times 2^{100} \\ &\approx 1.27 \times 10^{30} \end{aligned} \]
\(2 \times 10^{10}\) and \(2 \times 10^{20}\) are far too small, since \(2^{100}\) is about \(10^{30}\), and \(1 \times 10^{50}\) is far too large. (In practice the culture would run out of nutrients long before, but the question asks for unrestricted growth.)
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