Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of

6.4
%

per hour. How many hours does it take for the size of the sample to double?
Note: This is a continuous exponential growth model.

Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

log(2)/log(1.064) ≈ 11.17 . . . . hours

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The population can be given by
p(n) = p₀×1.064ⁿ . . . . where n is the number of hours
You want to find n whe p(n) = 2*p₀.
2p₀ = p₀×1.064ⁿ . . . . . . . . . . . . substitute the given information
2 = 1.064ⁿ . . . . . . . . . . . . . . . . . divide by p₀
log(2) = n×log(1.064) . . . . . . . . take logs to make it a linear equation
log(2)/log(1.064) = n . . . . . . . . divide by the coefficient of n