Questions: 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 1.8% per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents, P(x), who regularly used the news outlet x years after 2000.
P(x)=
Transcript text: ore on Slope
Question 4, 2.4.25
HW Score: $60 \%, 3$ of 5 points
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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 $1.8 \%$ per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents, $\mathrm{P}(\mathrm{x})$, who regularly used the news outlet $x$ years after 2000 .
\[
\mathrm{P}(\mathrm{x})=\square
\]
(Use integers or decimals for any numbers in the expression.)
Solution
Solution Steps
Step 1: Identify the Initial Percentage
The initial percentage of residents using the news outlet in the starting year is 52%.
Step 2: Determine the Average Rate of Change
The average rate of change in the percentage usage per year is -1.8.
Step 3: Construct the Linear Function
The linear function modeling the percentage of residents using the news outlet is given by:
$$P(x) = -1.8x + 52$$
Step 4: Model the Percentage of Residents Using the News Outlet
After 23 years, the percentage of residents using the news outlet is approximately 10.6%.
Final Answer:
The model predicts that 10.6% of residents will be using the news outlet 23 years after the starting year.