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

• describe an appropriate domain and range for the function.
• make a rough sketch of a graph of the function.
• briefly discuss the validity of the graph as a model of the true function.

. briefly discuss the graph. choose the correct answer.
a. the validity of the graph as a model of the true function can never be known.
b. the graph is not a valid model of the true function.
c. the graph is a valid model of the function because the time in hours increases as bacteria increases.
d. the graph is a valid model of the function because the number of bacteria increases as number of hours increases

Explanation:

To determine the validity of the graph as a model for the function (time, number of bacteria), we analyze the relationship between time (in hours) and the number of bacteria. Bacteria typically grow over time, so as the number of hours (time) increases, the number of bacteria is expected to increase. Option D correctly states this relationship, making it a valid model. Option A is incorrect because we can assess validity based on known growth patterns. Option B is incorrect as the graph can be valid. Option C misstates the relationship (time doesn't increase because bacteria increases, but bacteria increase with time).

Answer:

D. The graph is a valid model of the function because the number of bacteria increases as number of hours increases