Problem 96 - Algebra and Trigonometry

Question

For the first 30 days of a flu outbreak, the number of students on your campus who become ill is increasing. Which is worse: The number of students with the flu is increasing arithmetically or is increasing geometrically? Explain your answer.

Step-by-Step Solution

Answer

A geometric (exponential) increase in the number of students getting sick would be worse, as it suggests a faster, uncontrolled spread of the disease.

Step 1: Define Arithmetic and Geometric Increase

In an arithmetic sequence, the increase is linear - each term increases by a fixed amount. For example, if five more students get sick each day,that would be an arithmetic increase. A geometric sequence, on the other hand, means an exponential increase - each term is multiplied by a certain amount. For example, if the number of sick students doubles each day, that would be a geometric increase.

Step 2: Analyze the Situation

Once we have defined the concepts, we analyze the situation presented in the exercise: that is, students at a campus are getting sick for a flu outbreak. We need to determine if a linear (arithmetic) or exponential (geometric) increase in sickness would be worse.

Step 3: Compare Arithmetic and Geometric Increase

In terms of the spread of a disease, a geometric increase is generally worse than an arithmetic increase. This is because an exponential (geometric) increase suggests that the disease is spreading faster, with more and more people getting sick each day. In contrast, a linear (arithmetic) increase suggests a steady, controllable rate of new cases.