The generation time G for a particular bacterium is the time it takes for the population to double.
The bacteria increase in population is shown by the formula G =
, where t is the time
3.310g.P
period of the population increase, a is the number of bacteria at the beginning of the time period, and Pis the number of bacteria at the end of the time period. If the generation time for the bacteria is 4.5 hours, how long will it take 4 of these bacteria to multiply into a colony of 7,525 bacteria?
Round to the nearest hour.
95 hours
132 hours
• 2 hours
O 57 hours
First, we need to determine the initial number of bacteria (a) and the final number of bacteria (P) using the information given.
Given:
Generation time (G) = 4.5 hours
a = 4 bacteria
P = 7,525 bacteria
Using the formula G = t/3.310g.P, we can find the time period (t) it takes for the bacteria to multiply from 4 to 7,525.
4.5 = t/(3.310 * 4 * 7,525)
4.5 = t/100,130
t = 4.5 * 100,130
t = 450,585 hours
So, it will take approximately 450,585 hours for 4 bacteria to multiply into 7,525 bacteria. Now, we need to round this to the nearest hour.
450,585 hours rounded to the nearest hour is 95 hours.
Therefore, it will take 95 hours for 4 bacteria to multiply into a colony of 7,525 bacteria.