Test%202%20Key

# Test%202%20Key - 1(8 2(12 3(9 Consider the curves in the...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1. (8) 2. (12) 3. (9) Consider the curves in the following ﬁgure. Match curves I, II, III and IV with the following formulas, where a is some constant strictly greater than 1. a. y=—ax§_]—_[I I II A population of 15 .8. million people grows at a constant percentage rate. Determine the size of the population 20 years later if there is: kt a. A continuous growth rate of 2.9%. '> DL+B= F0 8 686109qu ___ £8.22 1%?”ka ' t b. An annual growth rate of 2.9%. ‘7' PG‘) = Po lo 15.6 (macaw: Rank the following three bank deposit options from best to worst. Show all work. . . 36:5 ' a. Bank A: 3.04% compounded daily Po U + 035 a: Loaocl b. Bank B: 3.1% compounded quarterly R; (1+ 333“ 7t l-03 l "l 0. Bank C: 3.06% compounded continuously pa 9080309 a: W Loan 4. (14) ' Solve the following equations for x. Solutions Should be exact. a. 5x =17 V M05)" = MM) )L 4:45) =1 MO?) «QUV’CQ‘Q \\ M {2%) = (ﬁx +7» ' M5140) i\ In (1W) ~ _,._. ' 01x6 MGMQ 5. (l4) Solve the following equations for x. Solutions should be exact. a. 51n(2x—3)=l7 H/S i? a +3 = ’5‘ X: \4/5 W 9‘ Qx—3= a J 7} 9~>L= 6‘ l5 *3 6. (12) In the following problems, convert to the form Q = ab’ an_d identify the annual percent rate K of growth or riecay. b 5 e/ a. Q = 6e0‘7' Q ; (Q (Q‘DMYC K - QD‘? A, .. 8 ' a "" ‘QDM "b [01.Lf°[oamm+k 't Q:QCQ.D[%> 2) 10: Hr a r = \o -l ' = 2.01% ~1 T— . ‘5. {OX .4 b. Q = 789‘3'4’ ‘ O “’i 7° 9:34 it .05?) =b Q = :Irg @0333" ——> F=.o%% -\ " " «We? 3 "(762370 7. (12) A family of rabbits begins with 6 rabbits. After 5 months, the family has grown to a size . of 176 rabbits. Assuming the growth is exponential: a. Give a formula for the number of rabbits as a function of time in the form R = ab’ . V 0t=C<> =92 l%=(¢2b"5, ‘32 Pia—:55 :e 302%ng ' t bx 1.3(2‘3‘ Q‘éU-CICQSB ‘L L} ﬁle; = (o (HMS) b. Give a formula for the number of rabbits as a function of time in the form R = 06“. b =el< 1% K = MUD} => K=lrt (HMS) % 0,0,}5 0197's 1: R = (o e ~ 0. How long Will it take for the family of rabbits to be 50 times its original size. (AM. anocan— [a °Fb)—~ r _ . (97151, usmé Q'CQ 9’ ‘ L \ SPEC; mold-l4) - (9751‘: v\ 50 eoo=Coe t-r w 253% . . (OK-t . 5' SD = 9/ MED) = tors-t 8. (16) Consider the function f (x) = J; — 3 . For each of the following, determine the formula of the new function and describe the transformation that has occurred to the graph of f (x) . New_ formula Descrition of Transformation y=f(x+2) st Lift annals y=f(x)—5 swat W 5 0MB y=_f(3x) Hort Compt‘QsSlEM by '/3 x— onaS meQd-Lém \j-CAKLS (VPch ‘ Var-H _ (moMSSLiN by ‘19. 9. (10) Determine the formula of the following parabola. {Ix} = OLLX-hl 'L +\< ammo—331 +6 5-— éuCo—gf +8) 5: *8) -3:ch é &.=”\/3 10. (10) Consider the ﬁgure of y = f (x) for the following: 8 . ﬁx) , 4’ Next consider the following transformation of f. 3! 12 (geriw i “x A; m m m mummy: m. m y = S 6 a “we 4 8 1216 2b a. Describe (in words) what transformations have occurred. ~> x—ooors (nﬂaclrm —> MAW straight by Q ‘CCLCiOV‘b *1 >2 Stu-H, 09 8 b. Find a possible formula for the transformation off shown. Given tiﬁ -. - , {IQ ——> )UOUQ'S (EV. -{3Cﬁg3 -—> horii. 6M 391x) +8) a cart. 51ch “Have 11. (10) For f (x) = x2 — 8x + 9 , convert the quadratic into vertex form by completing the square. Then identify the vertex and the axis of symmetry. anauagar4%r%Mua ADM =w 4o +q rm: (wait—:6 12. (12) 13. (11) Using the given triangle, ﬁnd the following: Solutions should be exact. . 01 a. s1noc= f’ H- 2W0 b. sinﬁ= T _ 2E5 c. cosa— #— H d. cosﬁ-e fa— A spider spins a single thread from the ground to the top of a nearby gravestone. If the length of the thread is 3 meters and the angle between the ground and the web is 32" , ﬁnd the height of the gravestone. Mo WW5 32° 7 51n(%1°3='*‘g” / 7 = 3~ men") x New Extra Credit (10 points) If you need \$23,000 eight years from now, What is the minimum amount of money you need to deposit into a bank account that pays 4.5% annual interest, compounded: At =Pl 3t ‘1 a (+r a. Annually? 8 93°00 : P OMS) \$ No 11% 2e _ 2300b A' ' ’ P' Lions)” " M7 W34“? aast M AL+§=P (warnsl b. Daily? ups Cg> ascoo=POVZjé , Macaw! 23000 @é We» :2 Howe-Cf! 0* aces c. If the interest in the account is compounded continuously and you only have \$15,000 to invest, how long will it take for your investment to grow to \$23,000? 230cc) = 15000 em“ , GHQ? SW5 (5000 MCza/ja m [‘4 = .Ol—i‘St =~> t; log—S A” ...
View Full Document

## This note was uploaded on 12/23/2009 for the course MTH 151 taught by Professor Mason during the Fall '09 term at VCU.

### Page1 / 7

Test%202%20Key - 1(8 2(12 3(9 Consider the curves in the...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online