This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ' 5
Somme/0 MATH 122, SECTION 021 TEST 113 You may use a calculator, but not the TI—89. Show all work for full credit. 1. Write the equation of the exponential function that passes through the points (37 270)
and (5,972). (8 points) 270: Be “3° 73.2. , lief 270: 3/5"“)
777= 172%) Z70 £6le
. a : 62K )2: 2K 051”:
£00.30 = 1/18 77: )2506
Maw ‘AE— all Z t
K; ,ﬂlsn P: 2. Complete the table of values. (6 points)
a. f is a linear function. u 18
\/7 ‘HO b. 9(30) is an exponential function. . mgrmm:
L/i il XLZ
3. Rewrite the function P = 200060‘48t in the form P = Pout. (8 points)
0H8
a:€’< ...—.> age P )t [+r= llaleDfl’
=20c>c> mole _
a= mum fO (0’00?
Fill in the blank: Annual Rate: 2’ Continuous Rate: M 4. Determine whether each of the following is a power function. For all power functions7
give the values of k: and p. (6 points) a. y = 2(75”) 0. y = 56/5
Net a Power ‘1 5 5X [/4
FuﬂC‘lTo’l
14= 5 2 5. Sam goes to Europe for Spring Break with $4500. Find a formula for the balance B of
his money after t days in Europe if he spends
a. 13% of his money each day. (4 points) B= L/Soo(a87)t b. $360 each day. (4 points)
B = 9500 — 3W 6. If an investment increases exponentially from $5000 in 2008 to $8400 in 2011, What is
the annual (not continuous) growth rate? (8 points) m=guzmw3 _ l+r=H8878
5030 5m
“08: as F=0JS$78 a= $1887? 7. Suppose your student organization decides to sell T—shirts to raise money. It costs a
total of $155 to produce 20 Tshirts and a total of $320 to produce 50 T—shirts. You decide you should sell the T—shirts for $8 per shirt.
a. Find a linear equation expressing the cost, C (q), of producing q shirts. (5 points) m: =55
5020 6 *155= 55320)
6155 = 5. — no b. Find the revenue function, R(q). (2 points) 0. How many Tshirts do you need to sell to make proﬁt? How did you determine this? 3 oint
( p S) We mush 56“ $\’ 82 6.52 +95
252 = 45
+8 mal‘C pr 3‘" 2H8 8. Suppose a company’s demand function is given by
q = —40p + 2200, Where p is the price at which q items will be sold. Determine the vertical intercept and
explain What this means for the company. (6 points) ?, ydoyzzoo Verbena ink/«pi? 2:2200 I? m rims are 55an W Page)
Hammers W“ alert/lama! 2200 lire/W5. 9. The size of a bacteria colony triples every 8 hours. If the bacteria is growing exponen—
tially, how long will it take the number of bacteria to be 5 times the original amount? I
(8 points) é 3:100
Le as) _ 0.13725
300:1086 . 5.095%
"’ 73?; ‘ mo "e‘;
3¢ 6 K 5: 6 0.13715
M3: l/hZ g ['46: M6
13 = 8" ’4—5 ‘ Dig—“ft
% a“ K K= 0J3? [a a=l./47> 10. The promoters of a local festival estimate that 25 hours after the doors open at 9AM, y‘
the attendance A of people at the festival can be estimated by A(t) = ~28t2 + 3922: + 25 people. Calculate the average rate of change in the attendance between 1PM and 6PM. Give units.
(8 points) w a M tag—49 5 /¥§§41ﬂ5= 25/50/16. 6PM —> £4 4 11. The distance an object falls is directly proportional to the square of the time that it has been falling. If an object falls 144 feet in 3 seconds, how far will it fall in 7 seconds?
Give units. (6 points) D: Ktz z ‘D ; )[piz
W“ K (5) 13551067); K: Mo b: 12. I am saving money for.retirement and my investment is growing exponentially. In the year 2003, I had $5,000. and by 2011, I had $12,000. If I can“ retire once I have $250,000, in
What year will I be able to retire? (10 points) ti 200319615=O . « \. m) ’ 0"ng
120w=5a3sea  Z@?$QO€
15;): San: _. 5000 5559 XL 50 v 0.10975 M2.” = W p . Lnéo= .lnc ’
[(12.4 =ﬁ/é . 2 ,2 /,,_5_c_3 = 0.49325
'2’?" a — valor (or a=/,Iw> £45.74? [can web/8 M 13. Determine the intervals over which f is increasing, decreasing, concave up, and
concave down. Give your answers in interval notatién. (8 points) Increasing: ’60 ’2 U (4 a)
Decreasing: _LZJ£___—_
Concave up: AW— Concave down: “as ‘ ...
View
Full
Document
 Spring '08
 KUSTIN

Click to edit the document details