Math Problem Statement
In 19981998, the percentage of 18- to 29-year-olds who used the Internet was 7171%. In 20072007, that percentage had risen to 8787%. Complete parts (a) through (d) below. Question content area bottom Part 1 a) Use the year as the x-coordinate and the percentage as the y-coordinate. Find the equation of the line that contains the data points. yequals=StartFraction 16 Over 9 EndFraction x minus 3481 16 9x−3481 (Type an exact answer. Do not include the % symbol in your answer.) Part 2 b) Use the equation in part (a) to estimate the percentage of Internet users in 20122012. The percentage of Internet users in 20122012 is approximately enter your response here%. (Simplify your answer. Use the answer from part (a) to find this answer. Round to the nearest tenth as needed. Do not include the % symbol in your answer.)
Solution
Part 1:
a) Finding the equation of the line:
To find the equation of the line, we will use the two points given, corresponding to the years and percentages:
and .
The slope of the line is calculated as:
Now, using the point-slope form of the equation of a line: Substitute and the point :
Now, solve for :
Distribute the :
Thus, the equation of the line is approximately:
Part 2:
b) Estimating the percentage of Internet users in 2012:
Now, use the equation and substitute to estimate the percentage for 2012.
Let me calculate this.The estimated percentage of Internet users in 2012 is approximately .
Would you like any further clarification or more details?
Here are 5 related questions:
- How do you calculate the slope of a line between two points?
- What is the point-slope form of a linear equation?
- How do you interpret the y-intercept in this context?
- How can linear interpolation or extrapolation be used in real-world predictions?
- What assumptions are made when predicting future percentages based on past data?
Tip: When solving for a line equation from data points, always verify whether the equation makes sense by substituting values to check consistency.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Interpolation
Extrapolation
Formulas
Slope formula m = (y2 - y1) / (x2 - x1)
Point-slope form y - y1 = m(x - x1)
Equation of a line y = mx + b
Theorems
Slope-Intercept Theorem
Point-Slope Form
Suitable Grade Level
Grades 9-12