Math 150 ~ Review for Exam #2
1. Use the square root property to solve 3x  1  12 .
2
2. Use the quadratic formula to solve x 2  5x  x  7 .


3. Solve x 2  4 x  3  0 analytically or graphically(show graph). 4. Divide. 18x 2  3x  2  3x  2
5. Use synthetic division to find P 2 for Px   5x 3  2 x 2  x  5 .
6. Find all zeros of analytically. P  x   2 x3  8x 2  11x  5
7. Factor Px   2 x 3  3x 2  5x  6 .
8. Find the cubic polynomial in standard form with real coefficients, given that 3  2i and 4 are zeros.
9. a) Find a polynomial function P of lowest possible degree, having real coefficients, given that 3  i and
 2 (multiplicity 2) are zeros. (You may leave it in factored form).
b) Find a polynomial P  x  with real coefficients that satisfies the given conditions:
Degree 5; zeros are 3, 0 of multiplicity 3, 2 ; and P 1  24 .
10. All work must have a valid reason. a) Solve. 5x 3  x 2  10 x  2  0
b) Solve. x 4  16
11. Use leading term analysis, end point behavior, and multiplicity of roots to draw a rough sketch of the
graph of the polynomial function P  x    x 
26
 3  x   x  2 5  x 
54
25
37
12. Ohm’s law states that the current I in a wire varies directly as the electromotive forces E and inversely as
the resistance R. If I =22 amperes when E= 110 volts and R = 5 ohms, find I if E = 220 volts and R = 11 ohms.
13. a) Find all asymptotes, holes (if any), x-intercepts (if any), y-intercept (if any), check whether the graph
crosses its horizontal asymptote, and graph the function f  x  
x2  1
x 2  4 x  21
b) Find all asymptotes, holes (if any), x-intercepts (if any), y-intercept (if any), check whether the graph crosses
x2  4
its horizontal asymptote, and graph the function f  x   2
x  4 x  12
c) Find all asymptotes, holes (if any), x-intercepts (if any), y-intercept (if any), check whether the graph crosses
its horizontal asymptote, and graph the function f  x  
x 2  2 x  15
x5
14. Solve the following equation and its related inequalities analytically:
a)
5x  2
2
2x  6
b)
5x  2
2
2x  6
15. Solve, by your choice. If you use a graph, then draw a quick sketch.
c)
5x  2
2
2x  6
2
3
 2
0
x  2x x  x
2
16.
The value of a Porsche Techart 993 t years after purchase is given by the function f (t )  100,0000.89t
a) Graph the function
b) Use the graph to estimate the value in 6 years.
c) Use the graph to estimate the half-life.
d) Estimate when the car will be worth $25,000.
17. a) Give the equation of the asymptote and graph y  2 x 5  3
b) Give the equation of the asymptote and graph y  log( x  5)  1
18. Solve.
1
19. Solve.  
2
1
 27 x
81
3 x 6
 8 x 1
20. Find the amount that will be in each account if $15,800 is invested at 4.6% annual interest for 6.5 years
compounded as given.
a) quarterly
b) continuously
c)find the doubling time for
compounding continuously.
21.
Annual passenger traffic (in millions) at LAX can be approximated by the formula
N (t )  58.7  2.3ln(2t  1) , where t is the number of years since 1990.
a) What is the likely annual passenger traffic in 2007?
22. Solve. log x 16 
4
3
b) Find N (25); verbally interpret.
23. Use the rules of logarithms to rewrite log 5
1
24. Rewrite as a single logarithm. 4 log 2 x  3 log 2 y  log 2 z  6 log 2 t
5
25. Find the domain of log(2x-3).
26. Use change of base to evaluate log 2 8 .
27. Solve (round to the nearest hundredth) a) 10e 3 x 7  5 b) e2 x  2e x  8
28. Find the domain and Solve. log 5 x  2  log 5 x  2  1
5 7
3m
29. Find the domain and solve. a) log 2 2 x   log 2 x  2  log 2 16
b) log 2 x 2  1 
1
2
2
30. a) The number of grams of a radioactive substance present after t hours is given by
A(t )  2500e 0.45t What is the half-life of the substance?
How long will it take for there to be 500 grams
left?
b) A bacteria culture doubles every 3 hours. If there are 100 bacteria to start then how many bacteria will there
be after 10 hours?
c) If the population of Mexico is around 106 million people now and if the population decreases continuously at
a relative decay rate of 1.17%, what will the population be in 8 years? Answer in millions.
31. The population of Brazil increased exponentially from 122 million in 1980 to 158 million in 1992.
a) Find the population continuous growth rate during that period. Use A  Pekt
b) Assuming that the population continues to grow at this rate, in what year will the population reach
220 million?
Math 114 ~ Review for Exam #2 Solutions

1  2 3 
1. 7. 

 3 
12
4. 6 x  5 
3x  2
6.
2. 3  2
3.  ,  3   1, 
5. P 2  25
7. Px   x  1x  22 x  3
 1 3 
5,

2 

8.

P  x   ( x  4)  x  (3  2i) x  (3  2i) 
9. a) Px   x  3  i x  3  i x  2
2
1

10. a)  ,  i 2 
5

b) P  x   6  x   x  3 x  2  6 x5  6 x 4  36 x 3
3
b)  2,  2i
11.
12. 20 amperes
13. a) V.A: x  7, x  3
H.A: y  1
x  int  1,1
1
y  int   
 21 
Crosses H.A @ x  5
b) V.A: x  6 ,
H.A: y  1
x  int  2
1 
y  int   
3
Doesn’t cross the H.A
c) V.A: none
H.A: none
x  int  3
y  int  3
Hole @  5, 8
1

Hole @  2, 
2

No holes
1
3
a) VA: x   , HA: y   , ask
2
2
14. a) x  14
b)  14,3
b) VA: x  1, OA: y  x  1 , ask
15. (−∞, 0) ∪ (1,2) ∪ [4, ∞)
16. A) around $50,000 b) about 6 years, c) about 12 years
c)
 , 14  3, 
17.a) y=-3, ask b) x=5, ask
18. -4/3
1 
19.  
2
20. a) $21,270.13
b) $21,306.45 c) about 15 years
21.a) 66.9 million, b) The Annual passenger traffic (in millions) at LAX in 2015 should be 67.7 million.
22. 8
1
23. 1  log 5 7  log 5 3  log 5 m
2
x4 5 z
24. log 2 3 6
y t
25. x  3 / 2
26. 1.5
27. a) 2.10 b) ln 4  1.386
29. a) 2 b) x  3,3
30. a) 1.54 hours, 3.58 hours
31. a) k  0.02155  2.155%
b) 1008 bacteria c) 96.53 million
b) t  27.4   in year 2007
28. 3