Quiz 3

Show all work in a neat and organized fashion. Clearly indicate your answers.

10 points possible.

Label all numeric answers. With models, give a concise explanation of the variables.

Example: Suppose a problem asks for a model, and suppose this is the answer:

Tax = 2538.90 + 540.37t dollars, where t is the number of years since 1989.

To receive full credit, this answer must include all of the following:

(1) the correct model (i.e., Tax = 2538.90 + 540.37t),

(2) the correct label for the output (i.e., ``dollars''), and

(3) the correct explanation of the input variable (i.e., ``where t is the number of years since 1989'').

Example: Here is another correct way to write the same answer.

D = 2538.90 + 540.37x, where D= dollars of tax, and x= number of years since 1989.

Year       Students                                   1965       5024       1966       5540       1967       6057       1968       6525       1969       7028

(a) Find a linear model for the data. Do not round.

(b) Use the model to estimate the enrollment in 1970. Round the answer appropriately.

(c) What is the rate of change of the model you found? (Include correct units.)

2. (5 pts.) The table below shows the enrollment for a university in the southeast from 1965 through 1969.

Population       Year       (thousands)                                   1985       677       1986       669       1987       661       1988       655       1989       646       1990       639       1991       633       1992       634       1993       635

(a) Observe a scatter plot of the data. Write down the values of Xmin, Xmax, Ymin, and Ymax that you used (press Window to see these values).

(b) From the scatter plot, what year is the dividing point that should be used to create a piecewise continuous function?

(c) Divide the data in the year you determined in part (b). Include the dividing point in both data sets. Fit linear models to each set of data, and write the function in correct piecewise continuous function notation. Round the numbers to four decimal places.