Question

In​ 2000, 49 % of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.3 % per year since then. Find a linear function in​ slope-intercept form that models this description. The function should model the percentage of​ residents, Upper P left parenthesis x right parenthesis comma who regularly used the news outlet x years after 2000.

Answer 1

The required function is P(x)=-1.3x+49.

Explanation:

Let P(x) be the percentage of​ residents who regularly used the news outlet x years after 2000.

It is given that in​ 2000, 49 % of the residents in a large city regularly used newspapers for getting news.

Initial percentage of​ residents who regularly used the news = 49

It has decreased at an average rate of approximately 1.3 % per year since 2000.

It is decreasing by 1.3% so,

`Slope=-1.3`

The slope intercept form of a line is

`y=mx+b` .... (1)

where, m is slope and b is y-intercept or initial value.

Substitute y=P(x), m=-1.3 and b=49% in equation (1).

`P(x)=-1.3x+49`

Therefore, the required function is P(x)=-1.3x+49.