Question

In​ 2000, 51 % of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.5 % 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.
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Part 1
​P(x)equals
  
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​(Use integers or decimals for any numbers in the​ expression.)

Answer 1

To find a linear function in slope-intercept form that models the percentage of residents who regularly used newspapers for getting news, we start with the information given:

- In 2000, \( P(0) = 51 \) (since \( x = 0 \) corresponds to the year 2000).
- The rate of decrease is 1.5% per year, which can be expressed as a slope of \( -1.5 \).

The slope-intercept form of a linear function is given by:

\[
P(x) = mx + b
\]

where:
- \( m \) is the slope,
- \( b \) is the y-intercept (the value of \( P(x) \) when \( x = 0 \)).

Using the data provided:
- \( b = 51 \)
- \( m = -1.5 \)

Now we can write the function:

\[
P(x) = -1.5x + 51
\]

Thus, the linear function that models the percentage of residents who regularly used newspapers \( P(x) \) after \( x \) years since 2000 is:

\[
P(x) = -1.5x + 51
\]