Question

In​ 2000, 52 % of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.6 % 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 (x )comma who regularly used the news outlet x years after 2000.

P(X) =

Answer 1

P(x) = -1.6x + 52

Explanation:

Let 2000 as the start point, so it will be the year 0, x = 0, and the population that uses newspaper (y) will be y = 52%. The slope of a linear function is how much it increases or decreases, so the slope is -1.6 (the minus signal indicates that it's decreasing). The slope can also be calculated by the equation:

a = Δy/Δx, where a is the slope, and Δy and Δx are the difference between two points in the function.

So, for x years, the population percentage will be y:

-1.6 = (y - 52)/(x - 0)

-1.6x = y - 52

y = -1.6x + 52

P(x) = y

P(x) = -1.6x + 52