The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of $1.1 \%$ per hour. How many hours does it take for the size of the sample to double?
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Note: This is a continuous exponential growth model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.
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$\square$
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Answer
Rounding to the nearest hundredth, the final answer is \(\boxed{63.01}\) hours.
Step 1 ：The continuous exponential growth model is given by the formula \(N(t) = N_0 * e^{rt}\), where \(N(t)\) is the final amount, \(N_0\) is the initial amount, \(r\) is the growth rate, and \(t\) is the time.
Step 2 ：In this case, we want to find the time it takes for the population to double, so \(N(t) = 2*N_0\).
Step 3 ：We can set up the equation \(2 = e^{1.1/100 * t}\) and solve for \(t\).
Step 4 ：Let \(r = 0.011000000000000001\)
Step 5 ：Solving the equation gives \(t = 63.01338005090411\)
Step 6 ：Rounding to the nearest hundredth, the final answer is \(\boxed{63.01}\) hours.
