Question

question
in a lab experiment, 650 bacteria are placed in a petri dish. the conditions
are such that the number of bacteria is able to double every 14 hours. how
many bacteria would there be after 7 hours, to the nearest whole number?
answer
attempt 2 out of 3
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Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is \(N = N_0\times2^{\frac{t}{T}}\), where \(N_0\) is the initial number of bacteria, \(t\) is the time elapsed, and \(T\) is the doubling - time. Here, \(N_0 = 550\), \(t = 7\) hours, and \(T=14\) hours.

Step2: Substitute the values into the formula

Substitute the values into the formula: \(N = 550\times2^{\frac{7}{14}}\).
Since \(\frac{7}{14}=\frac{1}{2}\), the formula becomes \(N = 550\times\sqrt{2}\).
We know that \(\sqrt{2}\approx1.414\).
So, \(N = 550\times1.414 = 777.7\).

Answer:

\(778\)