Question

A biologist puts an initial population of 500 bacteria into a growth plate. The population is expected to double every 4 hours. Which of the following equations gives the expected number of bacteria, n, after x days? (24 hours = 1 day)

a. n = 500(2)^x
b. n = 500(2)^6x
c. n = 500(6)^x
d. n= 500(6)^2x

Answer 1

The correct equation for the expected number of bacteria after x days, given they double every 4 hours starting with 500 bacteria, is n = 500(2)^6x.

Step-by-step explanation:

The biologist's question asks us to determine the equation that gives the expected number of bacteria, n, after x days, given that the population doubles every 4 hours. To find the correct equation, we need to consider how many doubling periods occur in a single day.


There are 6 doubling periods in a day (since there are 24 hours in a day and the population doubles every 4 hours). Therefore, after x days, there would be 6x doubling periods. The initial bacterial population is 500, so we use the formula for exponential growth:

n = 500(2)^(6x)

This equation correctly accounts for the number of doublings that occur every day and matches one of the given options, which is:

b. n = 500(2)^6x