To find the linear function that models the number of people afflicted with the common cold (C) as a function of the year (t), you can use the point-slope form of a linear equation:
C = mt + b
Where:
C = the number of people afflicted with the common cold
t = the year (starting from 2004)
m = the slope of the line (rate of decrease in cases per year)
b = the initial number of cases in 2004
You have the data for 2004:
- In 2004 (t = 0), there were 875 people afflicted (C = 875).
You also mentioned that the number of cases dropped steadily by 50 each year. This means the slope (m) is -50 (negative because the number is decreasing by 50 each year).
Now, you can plug these values into the equation:
875 = -50(0) + b
Simplify:
875 = b
So, b = 875.
Now you have the linear function that models the number of people afflicted with the common cold as a function of the year:
C = -50t + 875
To find out when no one will be afflicted (C = 0), you can set C to 0 and solve for t:
0 = -50t + 875
Subtract 875 from both sides:
-875 = -50t
Now, divide by -50 to solve for t:
t = -875 / -50
t = 17.5
So, in the year 2021.5 (or halfway through 2021), no one is predicted to be afflicted with the common cold according to this linear model. Since years are typically whole numbers, you can round up to the nearest whole year, which means no one will be afflicted in 2022.