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The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria increase in population is shown by the formula (see image) , where t is the time period of the population increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the end of the time period. If the generation time for the bacteria is 6 hours, how long will it take 8 of these bacteria to multiply into a colony of 7681 bacteria? Round to the nearest hour.

A. 177 hours
B. 76 hours
C. 4 hours
D. 85 hours

The generation time G for a particular bacteria is the time it takes for the population to double The bacteria increase in population is shown by the formula se class=

Respuesta :

wizard123
From the formula, solve for 't'
[tex]t = (G)(3.3 log_a (P))[/tex]

Substitute in given information
[tex]t = (6)(3.3) log_8 (7681)[/tex]

Rewrite log in terms of natural log using change of base formula
[tex]t = (6)(3.3) \frac{ln 7681}{ln 8}[/tex]

Compute with calculator
[tex]t = 85.19[/tex]

Final answer:
85 hours

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