1. The Multiple Risk Factor Intervention Trial (MRFIT) used data from 356,222 men aged 35 to 57 to investigate the relationship between serum cholesterol and coronary heart disease (CHD) risk. The following figure shows the graph of the relationship of CHD risk and cholesterol, where a risk of 1 is assigned to 200 mg/dl of serum cholesterol and where the CHD risk is 4 times as high when serum cholesterol is 300 mg/dl.

(a) Does this graph indicate that the CHD risk is a function of the serum cholesterol?
(b) Is the relationship a linear function?
(c) If CHD risk is a function f of serum cholesterol, what is f(300)?
2. When a couple purchases a home, one of the first questions they face deals with the relationship between the amount borrowed and the monthly payment. In particular, if a bank offers 25-year loans at 7% interest, then the data in the following table would apply.
Amount Borrowed _________________ Monthly Payment
$40,000 .............................................. $282.72
50,000 ................................................ 353.39
60,000 ................................................ 424.07
70,000 ................................................ 494.75
80,000 ................................................ 565.44
90,000 ................................................ 636.11
100,000 .............................................. 706.78
Assume that the monthly payment P is a function of the amount borrowed A (in thousands) and is denoted by P = f(A), and answer the following.
(a) Find f(80).
(b) Write a sentence that explains the meaning of f(70) = 494.75?
3. Suppose that the profit from the production and sale of x units of a product is given by
P(x) = 330x - 0.05x2 - 5000
In addition, suppose that for a certain month, the number of units produced on day t of the month is
X = q(t) = 100 + 10t
(a) Find (P q)(t) to express the profit as a function of the day of the month.
(b) Find the number of units produced, and the profit, on the fifteenth day of the month?

Transcribed Image Text:

4.0 4.0- 3.0 2.0 2.0- 0.7 1.0 1.0 + 100 150 200 250 300 Serum cholesterol (mg/dl) CHD risk ratio