Image description: A cartoon illustration shows a doctor pointing to a screen of an enlarged virus cell. The image on the screen changes to show a sick student in school.
Narration: The flu virus is more aggressive than the common cold virus. Suppose a student comes to school with a particular strain of the flu virus. We can use mathematics to study the growth of this flu virus.
Image description: An illustration representing 600 students in shown. As the doctor describes the number of students who catch the virus, that number of students is faded black in the illustration.
Narration: Let’s say that the school has 600 students. On the first day of school, one student has the flu. Each day, the number of sick students doubles. The pattern shows the number of students who catch the flu. 1, 2, 4, 8, 16, 32, 64, and so on. This flu virus spreads in a multiplicative pattern.
Image description: The words multiplicative pattern, geometric pattern or geometric sequence appears.
Narration: This is a type of geometric pattern, or geometric sequence.
Image description: A table with eight columns and two rows appears. The top row is labeled “Day” and increases from 0 to seven in increments of one. Plus 1 appears between each set of numbers in the top row. The bottom row is labeled “Number of sick students” and the eight columns show 1, 2, 4, 8, 16, 32 and 64. The common ratio of times 2 appears beneath the bottom row under each pair of numbers.
Narration: The flu virus in the example grew by a factor of two for each day that passed. This factor of two is known as the common ratio. If you divide a term in the pattern by the previous term in the pattern, you will obtain the common ratio.
Image description: 4 divided by 2 equals 2 is shown to represent an example of how to find the common ratio.
Narration: Compare the growth of the cold virus to the flu virus.
Image Description: Two tables are shown. The first table, labeled Cold Virus, shows two columns and seven rows. The first column is labeled Day and the second column is labeled Number of Sick Students: First row, Day 1, 1 sick student; Second row, Day 2, three sick students; Third row, Day 3 five sick students; Fourth row, Day 4, seven sick students; Fifth row, Day 5, nine sick students; Sixth row, Day 6, eleven sick students; Seventh row, Day 7, thirteen sick students. The second table, labeled Flu Virus, shows two columns and seven rows. The first column is labeled Day and the second column is labeled Number of Sick Students: First row, Day 1, one sick student; Second row, Day 2, two sick students; Third row, Day 3 four sick students; Fourth row, Day 4, eight sick students; Fifth row, Day 5, sixteen sick students; Sixth row, Day 6, thirty-two sick students; Seventh row, Day 7, sixty-four sick students.
At first, students seem to contract the cold much more quickly than the flu. However, after Day 4, the flu virus quickly overtakes the cold virus by making far more students sick with the flu than a cold.
Image description: The doctor points to each row to illustrate how the flu virus begins to spread more quickly than the cold.
Narration: Multiplicative patterns are also known as geometric sequences.