Exam 1: Linear Functions

A book publisher found that the cost to produce 1000 calculus textbooks is $25,600, while the cost to produce 2000 calculus textbooks is $50,300. Assume that the cost C(x)is a linear function of x, the Number of textbooks produced. What is the marginal cost of a calculus textbook?

Find an equation in slope-intercept form (where possible) for the line. -Through $(-5,4), \mathrm{m}=3$

Graph the equation. -y + 2 = 0

Suppose that the population of a certain town, in thousands, was 105 in 1990 and 141 in 2002. Assume that the population growth can be approximated by a straight line. Find the equation of a Line which will estimate the population of the town, in thousands, in any given year since 1990.

Find the correlation coefficient. -The test scores of 6 randomly picked students and the number of hours they prepared are as follows:

Find the slope of the line. -The x-axis

Solve the problem. -For the following table of data, a. Draw a scatterplot. B. Calculate the correlation coefficient. C. Calculate the least squares line and graph it on the scatterplot. D. Predict the y-value when x is 11.

Find the equation of the least squares line. -The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters).

Write a cost function for the problem. Assume that the relationship is linear. -A toilet manufacturer has decided to come out with a new and improved toilet. The fixed cost for the production of this new toilet line is $16,600 and the variable costs are $70 per toilet. The Company expects to sell the toilets for $155. Formulate a function C(x)for the total cost of Producing x new toilets and a function R(x)for the total revenue generated from the sales of x Toilets.

Solve the problem. -The bank's temperature display shows that it is 22° Celsius. What is the temperature in Fahrenheit?

Solve the problem. -A shoe company will make a new type of shoe. The fixed cost for the production will be $24,000. The variable cost will be $34 per pair of shoes. The shoes will sell for $100 for each pair. How Many pairs of shoes will have to be sold for the company to break even on this new line of shoes?

The temperature of water in a certain lake on a day in October can be determined by using the model y = 15.2 - 0.537x where x is the number of feet down from the surface of the lake and y is the Celsius temperature of the water at that depth. Based on this model, how deep in the lake is the Water 10 degrees? (Round to the nearest foot.)

Solve the problem. -The cost of owning a home includes both fixed costs and variable utility costs. Assume that it costs $5682 per month for mortgage and insurance payments and it costs an average of $1.35 per unit for Natural gas, electricity, and water usage. Determine a linear equation that computes the annual cost Of owning this home if x utility units are used.

Find the correlation coefficient. -The test scores of 6 randomly picked students and the number of hours they prepared are as follows:

Evaluate the function as indicated. -Find $g\left(\frac{7}{3}\right)$ when $g(x)=7-9 x$ .

Why is the slope of a horizontal line equal to zero? Give an example.

Solve the problem. -Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained Regarding their GPAs on entering the program versus their current GPAs. Use the equation of the Least squares line to predict the current GPA of a student whose entering GPA is 3.9.

Graph the equation. -5x + y = -4

Solve the problem. -The change in a certain engineer's salary over time can be approximated by the linear equation y = 1500x + 47,500 where y represents salary in dollars and x represents number of years on the job.According to this equation, after how many years on the job was the engineer's salary $64,000?

Can an equation of a vertical line be written in slope-intercept form? Explain.