Question

for the given function, use your intuition or additional research, if necessary, to complete parts (a) through (c).
(time, number of bacteria), where time is measured in hours of a day
a. describe an appropriate domain and range for the function.
b. make a rough sketch of a graph of the function.
c. briefly discuss the validity of the graph as a model of the true function.

a. choose the appropriate domain for the function.
○ a. the domain is all bacteria during a given day, or 5 cells to 120 cells.
○ b. the domain is all bacteria during a given day, or 10 billion cells to 25 billion cells.
○ c. the domain is all hours in a day, or 1 to 24 hours.
○ d. the domain is all hours in a day, or 25 to 36 hours.

Explanation:

The function is defined as (time, number of bacteria), where time is measured in hours of a day. The domain of a function represents the set of input values. Here, the input is time (in hours of a day). A day has 24 hours, so the domain should be the hours in a day, typically from 1 to 24 hours. Option A and B incorrectly define the domain as the number of bacteria (which is the range, not the domain). Option D has an incorrect range of hours (25 - 36 is more than a day). So Option C is correct.

Answer:

C. The domain is all hours in a day, or 1 to 24 hours.