MATH 1113
1. (2, 1)
Key to Exam #2 Review
2. (-4, 3)
3. No solution
4. 200 units
5. equilibrium price: $100 per unit; equilibrium quantity: 70 units
6. equilibrium price: $4 per half gallon; equilibrium quantity: 300 half gallons
7. Let x = amt. invested at 6%, and let y = amt. invested at 10%;
x  y  25,000; 0.06 x  0.10 y  2220 ; He invested $7000 at 6% and $18,000 at 10%.
8. x  2 ; (2, )
9. 83  x  113 ;
[83, 113)
10. 500 x  437,500  150 x ; They must sell more than 1250 logic boards to make a profit.
11. 6400  0.35m  2200  7100 ; She can drive between 12,000 and 14,000 miles.
12.a) 50 units
b) (50, ) c) (50, 350)
C ( x)  6.6 x  20
e) R( x)  7 x
d) (50, ) or x  50
13. They must produce and sell at least 268 units.
14.a) concave up
b) minimum
c) (1, -3)
15.a) concave down
b) maximum
c) (-8, 8)
16.a) concave up
b) minimum
c) (-3, -30)
17. x-int: -1, -7; y-int: 7;
vertex: (-4, -9)
17.
18.
19.
18. x-int: 0, 6; y-int: 0;
vertex: (3, 9)
19. x-int: none; y-int: 7;
vertex: (2, 3)
20. 2000 units, maximum profit $37,000
21. 200 units; minimum cost $3400
22. {-3, 2}
23. {0, -3}
27. {10, 4}
28. 1  5


3 3
24.  , 
5 5 
  5  i 31 
29. 

4


25. {±2}

26.  2i 10
1

30.  5, 
4


31. a) P( x)  2 x 2  220 x  2000
b) $4050 thousand
c) 10 units or 100 units
32. Equilibrium quantity: 600 units; Equilibrium price: $5800
33. a)
34.a) f (7)  46
c) f (7)  7.38; f (4)  6.60
b) concave down
b) f (3)  6
c) f (0)  3
d) f (4)  3
e) f (7)  3
b) f (50)  31928 , which means that in 1850, the U.S. population was
approximately 31928 thousand, or 31,928,000.
c) It predicts the population in 2050 to be about 278157 thousand, or 278,157,000.
35. a) power function
36. a)
b) decreasing
c) about 48.5%