Q19. - Algebra 2

Question

For exercise 19 and 20, use the table that shows the percent of people age 25 and over with a high school diploma over the last few decades.

19. Use a prediction equation to predict the percent in 2010.

Step-by-Step Solution

Answer

The model predicts that  $96.1\%$ of people will have a high school diploma in 2010.

Step-1 – Determine the points.

Consider Year as x coordinate and Percent as y coordinates

Use the points $(1975,62.5) and (1995,81.7)$ to determine the equation of the line.

Step-2 – Determine the equation.

The point slope form is $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

 

Substitute $\left(x_1{y}_1\right)=(1975,62.5) and \left(x_2{y}_2\right)=(1995,81.7)$ into the above formula.

$\begin{array}{l}y-62.5=\frac{81.7-62.5}{1995-1975}(x-1975)\\ y-62.5=\frac{19.2}{20}(x-1975)\\ y-62.5=0.96(x-1975)\\ y-62.5=0.96x-1896\\ y=0.96x-1833.5\end{array}$

Step-3 – Model prediction.

We need to predict the percent in 2010.

Put 2010 for x into the equation $y=0.96x-1833.5$.

$\begin{array}{l}y=0.96\left(2010\right)-1833.5\\ y=1929.6-1833.5\\ y=96.1\end{array}$

The model predicts that  $96.1\%$ of people will have a high school diploma in 2010.