Exam 2: Rates of Change and Linear Functions

Find the equation of the line with slope and goes through the point (9, 15). Write the answer in slope-intercept form.

Are these points collinear? (7, -8), (9, -10), and (11, -11)

The following equation represents the best-fit regression line for median personal total income of adult males vs. years of education past eighth grade in Northern Wisconsin. Median personal income = 5,813 + 5,567 years of education What would be the expected annual personal income of a male who had 8 years of education past eighth grade?

Find the slope of the line that passes through the points (7,-8) and (27,4).

The data below gives the mean annual cost for tuition and fees at private four-year colleges in the United States since 1980. It is clear that the cost of education is going up. Mean Cost of Tuition and Fees for Private Colleges A) Using Linear Regression techniques, find the linear equation that is the best fit to this data. Find the annual costs, C, at private four-year colleges in the United States as a function of the number of years after 1980, y. B) If costs continue to rise at the same rate, what would be the approximate cost in year 2010?Round values to 2 decimal places, if necessary.

A company has fixed costs of $24,000 per month and variable costs of $5.10 per unit manufactured. (Fixed costs are those that occur regardless of the level of production. Variable costs depend on the number of units manufactured.) A) Find a formula that describes the total monthly costs, C, for the company as a function of the number of units manufactured, x.Write your answer in slope-intercept form, . B) If the company manufactures 600 units what will their monthly costs be? C) If the company has $27,570 available to cover the monthly costs, how many units can the company manufacture?

When a large airliner approaches an airport, it begins its descent from about 100 miles away and takes about 20 minutes to descend from an altitude of 36000 feet. Assume that the airliner's distance to the airport is a linear function of the time, t (minutes), since it began its descent. A) Express as a function of t (minutes). Write your answer in slope-intercept form. B) Now find the airliner's altitude, A, as a function of the airliner's distance from the airport, d. Write your answer in slope-intercept form.

A used car salesman earns a salary, S, of $200 per week plus a commission of $55 for each car he sells, c.. A) What is the dependent variable? B) What is the independent variable? C) Find a mathematical model that gives weekly salary, S, as a function of number of cars sold, c.

The amount of money spent on food (F) each month for the average household is F(c) = 344.05 + 93.07c. Where c is the number of children in the household. Estimate the number of children in a household that spends $809.40 per month on food. (Round the answer to the nearest whole number.)

The function, , gives the weight (in ounces), w, of a cat that is a years of age. What are the units of the 3.5 in the formula?

The following table shows the number of new AIDS cases reported in Florida from 1986 to 1994. Calculate the average annual rate of change of new AIDS cases per year from 1986 to 1994. Round your answer to 2 decimal places, if necessary.

Find the value of x so that the line through the points (2.9,-0.8) and (x,-44.3) has slope 5.

Use the following to answer questions A contractor charges by the square foot for pouring concrete sidewalks and driveways. -If a 258 square foot driveway costs $1,328.70 and a 379 square foot driveway costs $1,951.85, what is the rate per square foot?

If the function is increasing, then the average rate of change is ___________ .

Which function's graph has a steeper slope?