Consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010, 12025 people are afflicted.

Question

Question 1: Find the linear function that models the number of people inflicted with the common cold, C, as a function of the year, t.

Question 2: Find a reasonable domain and range for the function C. Explain.

Question 3: If the function C is graphed, find and interpret the x and y-intercepts.

Answer 1

A linear equation written in slope-intercept form, i.e., y = mx + b, can be used to model real-life situations. The value of m represents the slope of the line, or the rate of change of y with respect to x. The value of b is the y-intercept, or the initial condition/amount. The rate of change here is the decrease in the number of people infected. Therefore, the slope would be negative. The y-intercept would be how many people were initially infected in the year 2005.