Salary after College. In 2010, Monster College surveyed 1250...

Salary after College. In $2010,$ Monster College surveyed 1250 U.S. college students expecting to graduate in the next several years. Respondents were asked the following question: What do you think your starting salary will be at your first job after college? The line graph shows the percentage of college students who anticipated various starting salaries. (TABLE NOT COPY) The mathematical model $$p=-0.01 s^{2}+0.8 s+3.7$$ describes the percentage of college students, $p,$ who anticipated a starting salary $s,$ in thousands of dollars. Use this information to solve Exercises $99-100$. a. Use the line graph to estimate the percentage of students who anticipated a starting salary of $\$ 30$ thousand. b. Use the formula to find the percentage of students who anticipated a starting salary of $\$ 30$ thousand. How does this compare with your estimate in part (a)?

Salary after College. In $2010,$ Monster College surveyed 1250 U.S. college students expecting to graduate in the next several years. Respondents were asked the following question: What do you think your starting salary will be at your first job after college? The line graph shows the percentage of college students who anticipated various starting salaries.
(TABLE NOT COPY)
The mathematical model
$$p=-0.01 s^{2}+0.8 s+3.7$$
describes the percentage of college students, $p,$ who anticipated a starting salary $s,$ in thousands of dollars. Use this information to solve Exercises $99-100$.
a. Use the line graph to estimate the percentage of students who anticipated a starting salary of $\$ 30$ thousand.
b. Use the formula to find the percentage of students who anticipated a starting salary of $\$ 30$ thousand. How does this compare with your estimate in part (a)?

Key Concepts

Substitution and Function Evaluation

Substitution is a fundamental technique used to evaluate functions at specific points. By replacing the variable with a given value in an equation, one can compute an exact outcome. This practice is essential in verifying model predictions against graphical estimates or other data analyses.

Mathematical Modeling

Mathematical modeling involves formulating real-world situations using mathematical expressions, equations, or formulas. In this context, a quadratic equation is used to approximate the relationship between starting salary and the percentage of students expecting that salary, showcasing how mathematical models can simplify and quantify observations from surveys or experiments.

Quadratic Functions

Quadratic functions are polynomial functions of degree two and are presented in the form ax² + bx + c. They can model various complex relationships and often produce parabolic graphs. In problems involving real-world data, such functions help to predict trends and calculate expected values based on given input variables.

Graphical Data Interpretation

Graphical data interpretation involves extracting numerical estimates or trends by visually analyzing charts or graphs. In survey problems and other data analysis scenarios, reading from a graph can provide an immediate, though sometimes approximate, understanding of the underlying distribution or relationship represented by the data.

Transcript

00:01 So to begin this problem, we were given a line graph that represents the anticipated starting salary at first jobs after college.

00:08 So if you notice in your graph, your x axis represents the anticipated starting salary, and your y axis represents the percent of college students.

00:17 So let's go ahead and take a look at part a.

00:22 Part a asks, use the line graph to estimate the percent of students who anticipate a starting salary of $30 ,000.

00:30 So i'm not going to redraw the graph for you, but if you look at your graph, you're given the estimated starting salary of $30 ,000.

00:38 So you would want to go to the right three units where it says $30.

00:42 Because remember, if you look at your units, it says that it's in terms of thousands.

00:47 So what you're going to do is go up from there and find the point.

00:50 Now, it's not exactly on a specific value.

00:53 However, it looks like it's between 20 and 24%.

00:57 And it actually kind of looks like it's about halfway.

01:00 So i would estimate that approximately 22 % of first jobs after college, people would think that they would earn approximately $30 ,000.

01:12 Now, let's go to part b in this problem.

01:15 Part b says we're going to use this formula.

01:18 P equals negative 0 .01 s squared plus 0 .8 times s plus 3 .7.

01:28 And we're told p represents the percent of college students and s represents the starting salary.

01:34 So they want us to use this formula to find the percent of students who anticipate a starting salary of $30 ,000.

01:41 So we're going to substitute 30 in place of s because again, that x axis is referring to the, if you look at the units, it's in terms of thousands...

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