Solve. Assume the exercise describes a linear relationship.
-In 2010 a certain county recovered $20 \%$ of its municipal wastes through recycling, up from $17 \%$ in 2005. Find a linear equation that fits this data. Use this equation to predict the percentage recycled in 2022 .
A) $27.2 \%$
B) $23.6 \%$
C) $28.9 \%$
D) $25.3 \%$

Question

Quizplus · Accepted Answer

The linear equation that fits the given data can be found by first determining the slope (rate of change) and then using one of the points to find the y-intercept. The slope (m) is given by the change in percentage over the change in years, which is $(20\% - 17\%)/(2010 - 2005) = 3\%/5 = 0.6\%$ per year. Using the point (2005, 17%), the equation of the line in the form $y = mx + b$ can be set up as $17 = 0.6(2005) + b$. Solving for $b$ gives the y-intercept. However, to simplify calculations and avoid dealing with large numbers for years, we can use the year 2005 as a reference point (x = 0 for the year 2005). Thus, the equation simplifies to $y = 0.6x + 17$, where $x$ is the number of years after 2005. For the year 2022, $x = 2022 - 2005 = 17$. Substituting $x = 17$ into the equation gives $y = 0.6(17) + 17 = 10.2 + 17 = 27.2\%$.

Solve Assume the Exercise Describes a Linear Relationship 20%20 \%20% Of Its Municipal Wastes Through Recycling, Up From

Solve Assume the Exercise Describes a Linear Relationship $20 \%$ Of Its Municipal Wastes Through Recycling, Up From