Question
In 2000, 48 % 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 left parenthesis x right parenthesis comma who regularly used the news outlet x years after 2000.
Question content area bottom
Part 1
P(x)equals
enter your response here
(Use integers or decimals for any numbers in the expression.)
Question content area bottom
Part 1
P(x)equals
enter your response here
(Use integers or decimals for any numbers in the expression.)
Answers
GPT-4o mini
To create a linear function that describes the percentage of residents in a large city who regularly used newspapers for getting news, we start with the information provided:
1. In 2000 (when \( x = 0 \)), 48% of the residents used newspapers.
2. The percentage decreases at a rate of 1.6% per year.
We can denote the percentage of residents who regularly use the news outlet as \( P(x) \), where \( x \) is the number of years after 2000.
The general form for a linear function in slope-intercept form is:
\[
P(x) = mx + b
\]
Where:
- \( m \) is the slope (rate of change),
- \( b \) is the y-intercept (initial value when \( x = 0 \)).
From the information given:
- The slope \( m = -1.6 \) (the negative sign indicates a decrease).
- The y-intercept \( b = 48 \) (the percentage in the year 2000).
Now, we can substitute these values into the slope-intercept form:
\[
P(x) = -1.6x + 48
\]
Therefore, the linear function that models the percentage of residents who regularly used newspapers \( P(x) \) is:
\[
P(x) = -1.6x + 48
\]
1. In 2000 (when \( x = 0 \)), 48% of the residents used newspapers.
2. The percentage decreases at a rate of 1.6% per year.
We can denote the percentage of residents who regularly use the news outlet as \( P(x) \), where \( x \) is the number of years after 2000.
The general form for a linear function in slope-intercept form is:
\[
P(x) = mx + b
\]
Where:
- \( m \) is the slope (rate of change),
- \( b \) is the y-intercept (initial value when \( x = 0 \)).
From the information given:
- The slope \( m = -1.6 \) (the negative sign indicates a decrease).
- The y-intercept \( b = 48 \) (the percentage in the year 2000).
Now, we can substitute these values into the slope-intercept form:
\[
P(x) = -1.6x + 48
\]
Therefore, the linear function that models the percentage of residents who regularly used newspapers \( P(x) \) is:
\[
P(x) = -1.6x + 48
\]