Question

The number of people afflicted with the common cold C in the winter months steadily decreased by 202 each year from 2005 until 2010. In 2005, 12,073 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. (Let t represent the number of years since 2005.)

Answer 1

`C(t)=-202t+12,073`

Explanation:

Let t represent the number of years since 2005.

We have been given that the number of people afflicted with the common cold C in the winter months steadily decreased by 202 each year from 2005 until 2010.

The number of people decreased in t years would be
`202t`.

We are also told that in 2005, 12,073 people were afflicted. So 12,073 will be initial value.

We will represent our given information in an equation as
`y=mx+b`, where,

m = Slope of line,

b = The initial value.

Since the number of people afflicted with the common cold C in the winter months steadily decreased, so slope will be negative.

Substitute the given values:

`C(t)=-202t+12,073`

Therefore, our required equation would be
`C(t)=-202t+12,073`.