Download final exam mat 98 set b name

FINAL EXAM MAT 98
SET B NAME: ________________
Total possible points: 110 points
1. (9 PTS)Simplify and write without negative exponents. Please show work:
 a 5 
(a)  2 
 3b 
3
1/ 2
 25x 5 
(b) 
4 
 xy 
(c)
2w3 ( w2 ) 3
5w5
2. (6 PTS) Suppose a $8000 car loses 11% of its value each year. Write an exponential equation
and use it to find how many years will the value be half of its original?
3. (6 PTS) Please show work. You may use your calculator program.
The height of an object thrown into the air follows the equation
h = -0.5gt2 + v0t + h0 where g is acceleration due to gravity (32.2 ft/sec2), v0 is the initial
velocity and h0 is the initial height.
If you throw a ball into the air with an initial velocity of 10ft/sec and assuming that the ball
leaves your hand at 5.1 ft, when will the ball hit the ground?
(round off your answer to 2 decimal places)
4. (12 PTS) Assume that all the variables represent positive real numbers. Perform the indicated
operations. Show work and simplify when necessary. Answers should be in SIMPLIFIED
EXACT form.

(c)
(c)
3
x  12

2
32x 4 y 6 z10
5. (9 PTS) Factor the following:
(a) x3 – 1/8
(b) 16x2-40x+25
(c) 4x2 – 25y2
(d) a 4 81ab  4 a5b
(d) 4 8  128  2 48  3 18
6. (12 PTS) Identify whether it is linear, quadratic, exponential or neither. Find the equation if it
is linear, quadratic or exponential. Please show work.
(a) 2, -7, -20, -37, -58, -83
(b) 1, ¼, 1/9, 1/16, 1/25
(c) 1/9, 1/3, 1, 3, 9
(d) –5.4, -4.8, -4.2, -3.6, -3, -2.4
7. (9 PTS)
(a) The pH of lime juice is 1.9. Calculate its hydrogen ion concentration and write in scientific
notation. Note: pH = -log [H+]
 I 
12 
 10 
(b) Find the intensity in scientific notation of a 230-decibel sound. Note: D = 10log 
(c) How many times stronger was the 2004 earthquake in Indonesia (magnitude of 9.3) compared
to the 2005 earthquake in Chile (magnitude of 7.9)? Round off to the nearest integer. M = log X
8. (5 PTS) Evaluate the following using your calculator:
(a) log3 81
(b) log11 11
(c) -40961/4
(d) 2 4 3  3 5 4
9. (24 PTS) Solve each equation algebraically. You may use your QUADRAT program.
Approximate to four decimal places:
log b m  log b n  log b mn
(a) 3x  2  81 x
(b)
3x  4  5 x  1
log b m  log b n  log b
m
n
log b m n  n log b m

by  x
log b x  y 

(d) x2 – 7x/3 = 2
(c) 10-1.2x = 30
(f) log3 ( x  2)  log3 ( x  1)  3
(e) log x + log (x + 2) = 2
10. (6 PTS) Find the amount of money in a savings account if $1200 is deposited at 6% interest
compounded quarterly and the money is left for 7 months. Round off to the nearest cent.
Show work.
r
S  P (1  ) nt
n
11. (6 PTS) Given f(x) = 2x2 – x – 1 , find the following:
(a) y-intercept in function notation form.
(b) x-intercepts in function notation form.
(c) The coordinates of the vertex in function notation form.
(d) The equation of the axis of symmetry.
(e) Sketch the graph.
12. (6 PTS) Find an equation of the line that contains the point (-4, 3) and is perpendicular to the
line 2x – 3y = 1.