Problem 96 - College Algebra

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

Geometric increase is worse than an arithmetic increase. This is because, in a geometric increase, the number of infected students would multiply, potentially leading to a faster and more drastic increase in cases each day.

Step 1: Understand Arithmetic Growth

Arithmetic growth is a sequence of numbers in which the difference of any two successive members is a constant. For example, the sequence 2, 4, 6, 8, 10 is an arithmetic sequence with the common difference of 2.

Step 2: Understand Geometric Growth

Geometric growth is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number. For instance, the sequence 3, 6, 12, 24, 48 is a geometric sequence with the common ratio of 2.

Step 3: Identify the Impact of Each Growth

To determine if arithmetic or geometric growth is worse in a flu outbreak, compare the two types of growth. With arithmetic growth, the number of people infected would merely increase by a constant amount. However, with geometric growth, the number of people infected would multiply - meaning each day, more people could get infected than the day before.

Step 4: Make a Conclusion

Geometric growth represents a more severe condition in a flu outbreak. It results in a faster and more significant increase in the number of infected students. The fact that the number of flu cases can potentially double, triple, or increase even more drastically with each passing day makes geometric growth worse than arithmetic growth in this situation.