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Unformatted text preview: SOLUT I 0/05 MATH 122, SECTION 021 TEST 1A 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 (2, 400)
and (5,204.8). (8 points) 204,8: PDCM(5) 5/:
204,8 3 Be 400 2"
He 3,: aSIZ = 6 men = Me (45,512 5 L
————3 if
K: '0123 ' 2. Complete the table of values. (6 points)
a. f is a linear function. .
Iii 31L b. g(x) is an exponential function. a me aa 990‘!
U XIH 3. Rewrite the function P = 1000(1.54)t in the form P 2 Poem. (8 points) we" —> /.5‘I=e" ltrﬂ'sLl
l4L5‘/=)n€K “O’SH
K=0A3l¥8 Fill in the blank: Annual Rate: Continuous Rate: 4 3 I Z 4. Determine Whether each of the following is a power function. For all power functions,
give the values of k and p. (6 points) a. y=% c. y=7(2”)
\1: gx’é AM a VMV Fmde 2 5. 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 horizontal intercept and
explain What this means for the company. (6 points) 0 :  90;” *ZZOO Hon zw’al Wemep‘rt E? ; ZZOO ﬁgs #0 —""‘ NW 3N lance 15 ea NM I ams‘mers L]
Q: 650 W!“ M loav‘ will:on 6. If an organization’s membership increases exponentially from 3500 members in 2006 to
5600 members in 2011, What is the annual (not continuous) growth rate? (8 points) 5%: 3530015 [+r= 1.0985(0
, 1.60;.a5 r: (1098507 a: 18560 20 7. Suppose your student organization decides to sell T—shirts to raise money. It costs a
total of $323 to produce 50 T—shirts and a total of $428 to produce 70 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: AC: 428*323 = 525 6‘323 = 525i " 26025 b. Find the revenue function, R(q). (2 points)
m c. How many T—shirts do you need to sell to make proﬁt? How did you determine this?
(3 points) 82: 5,252 was we mob): sen at \easi'
2752 :éas
l‘D Male (Owed: i=zz 3 8. Sarah goes to Mexico for Spring Break with $2200. Find a formula for the balance B of her money after t days in Mexico if she spends
a. 15% of her money each day. (4 points) B = ZZCO(0. Set b. $286 each day. (4 points) 84200—2850»: 9. I am saving money for retirement and my investment is growing exponentially. In the
year 2005, I had $5,000 and by 2011, I had $11,000. If I can retire once I have $250,000, in What year Will I be able to retire? (10 points) 1cm) amt
“000: geese Zsoaoo = 520.216
5:100 599° 6/535 5339
(at 0.1316 : e L a z 6 0l5lt
é) ,
M22 = Me MSG = W tzz=é£ my 0%}
. K [or 4: [,HO) 2 Cam V‘Cl'l’e "4 10. The promoters of a local festival estimate that t hours after the doors open at 9AM,
the attendance A of people at the festival can be estimated by A(t) = —28t2 + 392t + 25 people.
Calculate the average rate of change in the attendance between 3PM and 7PM. Give units.
(8 points) 3PM —> bio AnaAw) : Ms Lam: _5C0M\e/ 4 11. The weight that can be supported by a 2—inch by 4—inch piece of pine (called a 2—by—4)
is inversely proportional to its length. If a 10—foot 2—by—4 can support 500 pounds, what
weight can be supported by a 8—foot 2—by—4? Give units. (6 points) \N=\<(}: w:5c:oo(Zl—
J.
500=K(ID) 12. The size of a bacteria colony doubles every 12 hours. If the bacteria is growing
exponentially, how long will it take the number of bacteria to be 7 times the original amount?
(8 points) ‘ 0.0578t
Let two EQ=~ISOe
1402) la) 0,0578t
755 es 0 057‘
2 ma M; :: Me
5 6
,zz 1A7 ; 0.054625
)n 2 = Inc ’— ‘ 1:— K [IT/1% [1% 7 kwﬂm Qw’wm t: 33,1088Ws 13. » Determine the intervals over which f is increasing, decreasing, concave up, and
concave down. Give your answers in interval notation. (8 points) :IIﬂIIIIIIIIIIII mem; 612)
mIIﬂIIIIIIIIIIII . Igﬁkliﬂgé—l_
IIHIIIIIIIIIIII Dmewe [email protected] a IIUIIIIIIII!III
_Illllllllllﬂill
_ IIIﬂIIIIIIﬂIINI
_ IIIHIIIIIﬂIIIlI IIIHIIIIIIIIII
_ IIIIIIIIHIIIII“ IIIINIIIIIIIII
IIIIIIIIIIIIIE‘
IIIIIIIIIIIIIII Concave up: M
Concave down: ‘ ‘ ...
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 Spring '08
 KUSTIN
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