Exam # 1A, Fall 2002 Name__________________

1. Each of the following formulas define a function. Identify the independent variable, the dependent variable and give the domain.

b)

2. In the following table, is Y a function of x?

3) Find the equation of the line with slope 25 and y-intercept equal to 100

Answer_y= 25x + 100_

4. The population of a certain town was 100 thousand in the year 1980 and increased

by 25 thousand each year thereafter.

Assume the annual rate of change in population remains constant. Let t be the number of years since 1980. That is, t = 0 corresponds to 1980.

a. Find the population function, P( t ) = P₀ + mt.

Answer P(t) = 100 + 25t or P(t)= 100,000 + 25,000t

b. Find the population that is predicted by your function in the year 2010.

Answer __850 thousand_

c. In what month of what year will the population reach 137?

Answer____June, 1981__

5) Find the equation of the line through the points (60 , 45) and (70 , 30).

Answer_y=45–1.5(x-60)_ or y=30-1.5(x-70) or y=-1.5x+135

6) The Bates Motel can rent 45 units at $60 per night and 30 units at $70.

1. Assuming that the number of units rented decreases at a constant rate as price increases, express the number, N, of units rented as a linear function

of the cost, c.

Answer_ N(c)= 45 –1.5(c-60) or N(c)= 30-1.5(c-70) or N(t)= -1.5c+135

 

2. Determine the price at which none of the units will be occupied?

7) The following table gives the population for City A from 1987 until the present.