Question

Consider this scenario: the number of people afflicted with the common cold C in the winter months steadily decreased by 203 each year from 2005 until 2010. In 2005, 12,096 people were afflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of the year t. If the function C is graphed, find the slope of the function_Interpret the slope of the function. For each year that passes, the number of people with the common cold _ by _

Answer 1

we have that

2005 ------> 12,096 people were afflicted -----> ordered pair (0,12,096)

2006 -----> 12,096-203=11,893 people ----> ordered pair (1,11,893)

Find out the linear equation

step 1

Find out the slope

m=(11,893-12,096)/(1-0)

m=-203/1

m=-203 people per year ---> is negative because is a decreasing function

step 2

Find out the linear equation in slope-intercept form

y=mt+b

where

m=-203

b=12,096 (initial value)

therefore

The linear equation is

y=-203t+12,096

The slope is -203 people per year

that means

For each year that passes, the number of people with the common cold decreases by 203