Question

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

Answer 1

From the formula, solve for 't'

`t = (G)(3.3 log_a (P))`

Substitute in given information

`t = (6)(3.3) log_8 (7681)`

Rewrite log in terms of natural log using change of base formula

`t = (6)(3.3) (ln 7681)/(ln 8)`

Compute with calculator

`t = 85.19`

Final answer:
85 hours