Test%202%20Key

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

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

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