4
(6 points) 1. Write the equation of the line with slope
passing through the point (3, 2). Express your
3
answer in point-slope form.
1.
(10 points) 2. Water is added to a barrel at a constant rate for 25 minutes, after which it is full. The quantity
of water in the barrel after t minutes is 100 + 4t gallons.
(a) What do the 100 and 4 mean in practical terms?
(a)
(b) How much water can the barrel hold?
(b)
(8 points) 3. Could the second row be a linear function of the first? Show your work with at least three
calculations.
x
y
0
1575
5
1660
10
1715
15
1750
3.
Page 1
Math 100A
Exam #3 (Continued)
(8 points) 4. How many solutions does each equation have?
(a) 5x − (x − 2) = 6 + 2x
(a)
(b) 7 + x − 3 = 3(x + 1) − 2x
(b)
(9 points) 5. If y is directly proportional to x, and y = 10 when x = 3,
(a) Find the constant of proportionality;
(a)
(b) Write a formula for y in terms of x;
(b)
(c) Find x when y = 8.
(c)
Page 2
Math 100A
Exam #3 (Continued)
(8 points) 6. Which line has the steepest descent from left to right? How do you know?
(a) y + 4x = 5
(b) y = 5x + 3
(c) y = 10 − 2x
(d) y = −3x + 2
6.
(9 points) 7. Consider the linear functions
f (x) = −2x + 4
5
g(x) = 2x − .
3
and
Graph the equations. What do their graphs tell you about the number of solutions of the
equation f (x) = g(x)?
y
✻
5
✲
−10
−5
5
−5
−10
Page 3
x
Math 100A
Exam #3 (Continued)
(6 points) 8. Write an equation in slope-intercept form for the line that contains the points (6, 8) and (8, 12).
8.
(10 points) 9. Let p(t) denote the population of Lincoln t years after 1990, in thousands of people. Write
a complete sentence about what the following expressions tell you about the population of
Lincoln.
(a) p(8) − p(0) = 20
(b)
p(10) − p(8)
=7
2
Page 4
Math 100A
Exam #3 (Continued)
(12 points) 10. A small band would like to sell CDs of its music. The business manager says that it costs $320
to produce 100 CDs and $400 to produce 500 CDs.
(a) Write a linear function to represent the cost, $C, of producing n CDs.
(a)
(b) Find the slope and the vertical intercept of the graph of the function, and interpret their
meaning.
(b)
(c) How much does it cost to produce 750 CDs?
(c)
(d) If the band can afford to spend $500, how many CDs can it produce?
(d)
Page 5
Math 100A
Exam #3 (Continued)
11. Consider a species of songbird which spends d hours each day defending its territory and s
hours each day singing (looking for mates). Suppose this species of bird must consume 5
calories for each hour spent singing and 10 calories for each hour defending its territory.
(4 points)
(a) If this species consumes 60 calories per day for these activities, find a constraint equation
relating s and d.
(4 points)
(b) Give two solutions to the constraint equation you found in part (a), and explain their
meanings.
(6 points)
(c) Graph the equation you found in part (a) with the solutions you found in part (b). Make
sure to label your solutions.
d
✻
10
✲
−20
−10
10
−10
−20
Page 6
s