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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 $6279_w98_h21.png$
Explaination

An exponential function can be written in the form $7024_w56_h20.png$ where a is the initial amount, b is the growth factor, and t is the time. In the scenario described, the variable y can be substituted with n, the total number of bacteria, and the initial amount is given as 500, which yields $8676_w75_h16.png$. The growth factor is 2 because the population is described as being expected to double, which gives the equation $3173_w90_h21.png$. The population is expected to double every 4 hours, so for the time to be x days, x must be multiplied by 6 (the number of 4-hour periods in 1 day). This gives the final equation $6279_w98_h21.png$.