Question

The number of people afflicted with the common cold in the winter months dropped steadily by 25 each year since 2002 until 2012. In 2002, 8,040 people were inflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of the year, t. When will less than 6,000 people be afflicted?

Answer 1

To find the linear function that models the number of people afflicted with the common cold C as a function of the year t, we need to determine the slope and y-intercept and apply them to the equation y = mx + b. The linear function is C = -25t + 58,090. Less than 6,000 people will be afflicted in the year 2,345.

Step-by-step explanation:

To find the linear function that models the number of people afflicted with the common cold C as a function of the year t, we need to determine the slope and y-intercept of the line.

First, we need to find the slope (m) of the line. The number of people afflicted with the common cold dropped by 25 each year since 2002 until 2012. This means that for every year (t) increase, the number of people afflicted (C) decreases by 25. So, the slope is -25.

Next, we need to find the y-intercept (b) of the line. In 2002, 8,040 people were afflicted. This gives us a point (2002, 8040) on the line. Using the slope-intercept form, we can substitute the values into the equation y = mx + b and solve for b. So, 8040 = -25(2002) + b. Simplifying, we get b = 8040 + 50,050 = 58,090.

Therefore, the linear function that models the number of people afflicted with the common cold C as a function of the year t is C = -25t + 58,090.

To find the year when less than 6,000 people will be afflicted, we substitute C = 6,000 into the equation and solve for t. So, 6,000 = -25t + 58,090. Simplifying, we get t = (58,090 - 6,000) / -25 = 2,345.

Therefore, less than 6,000 people will be afflicted in the year 2,345.