Suggested Answers for Problem Set #1 Professor Scholz
1) Portray the following hypothetical data on a two-variable diagram: Enrollment Data: Nowhere U Academic Year 2000-01 2001-02 2002-03 2003-04 2004-05 Total Enrollment 3000 3100 3200 3300 3400 Enrollment in Economics Courses 300 325 350 375 400
Measure the slope of the resulting line, give an algebraic representation of the line, and explain what the slope means. Answer: Find the slope of the line (call it m). Let Y = enrollment in econ courses; Let X = total enrollments. The slope is the rise over run, or, in this case, 1/4. Find the equation of the line in slope-intercept form: take any point (we’ll take (3200, 350) and use the formula Y = mX + b; and you found the slope (1/4) in the previous part of the problem. Therefore, 350=(1/4)*3200 + b, which implies b = -450. So the equation for the line is y = (1/4)*X - 450. The slope (1/4) means that enrollment in economics courses increase by 1 person every time total enrollment increases by 4 people. 2) Graph the following two equations on the same graph, X = 440 - 4Y and X = 40 + 4Y. Solve these two equations for X and Y. Do the graphing. The solution, solving the two equations for the two unknowns, are X=240 and Y=50. 3) Sam believe that the number of job offers he will get depends on the number of courses in which his grade is B+ or better. He concludes from observation that the following figures are typical: Number of grades of B+ or better Number of job offers 0 1 1 3 2 4 3 5 4 6
Plot these numbers on a graph. Measure and interpret the slopes between adjacent dots. Plot the set of ordered pairs (with job offers on the vertical axis and grades B+ or better on the horizontal axis). You’ll see that with Sam’s first B+ he gets a “big” jump in the number of job offers (2). Beyond the first B+, every additional B+ nets him one additional job offer. 4) Graph the following two equations on the same graph, X...