MATH 111 F2013 Practice Test 2a (Ch. 2-3) NameSHOW ALL WORKNO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK4 points each1. The following table shows the number of new AIDS cases reported in Florida from1986 to 1994.Year New AIDS Cases1986103 I1987 t6331988 265019893W1990 4018t99t5471t99z 5086t993 109581994 86t7Calculate the average annual rate of change of new AIDS cases per year from 1986 to1993. noundyour answer to 2 decimal places, if necessary2. Find the average rate of change of the function y = 8 * 2* between x: 0 and x: 4.3, Use the graph below to find the average rate of change of the function between x = 3and x:6 (1 cell: 1 unit).4. Find a linear function whose values are siven in the table below. rrn(r aare grven ulx-4 026f(x) 6 -6-12-245. In 2000 thsre were 39.8 million Americans without health insurance. This number hasincreased at an average rate of 1.7 million people per year.a) Write a formula that models the number of Americans without health insurance x yearsafter 2000.b) Find the number of Americans without health insurance in2012.6. Find an equation of the line that passes through (5, 6) and (7, -3).7 . y is directly proportional to x and y is 45.6 when x is 6.a) Find a formula to describe y as a function ofx.b) Use the formula to findy when x is 10.8. Find an equation of the line that is perpendicular to x + 4y: 8 and passes through(-3, 1).9. You invested $7000 in two funds paying 6%o and 80/o annual interest, respectively. Atthe end of the year the total interest from these investments was $520. How much wasinvested at eachrate?10. The length of a rectangular soccer field is twice as long as it is wide. If the perimeterof the field is 300yards, what are its dimensions?11. In 2010 there were 13,000 students at college A, with a projected enrollment increaseof 1000 students per year. In the same year there were 16,500 students at college B, witha projected enrollment increase of 500 students per year.a) Find the functions modeling college enrollment for each college, let x be the number ofyears after 2010.College A:College B:b) In what year will the colleges have the same enrollment?c) What will be the enrollment in each college at that time?12. Find the equationf(x) : Ca* for the function given by the table below.x f(x)-1 20 2.74I 3.752 5.t4Round values to 2 decimal places.13. a) Find an exponential function,f(x) : Ca', such that /(0) =31,000 and for everyunit increase in x, the output decreases by 20%.b) Find the value of the function when x : 10.14. A population decreases exponentially from 14,000,000 to 9,790,000 in 6 years.a) Find the 6-year decay factor.b) Find the yearly decay factor.Round onswers to 2 decimal places.15. rJse the compound interest formula A(t) : P(I + r;'' . Find the accumulated value ofnan investment of $5000 for 5 years ifa) the interest rate is 5.5% compounded semiannuallyb) the interest rate is 5.25% compounded monthly.16. In 1990 the population of Europe was 509 million and in 2000 it was 729 million.Find the exponential growth model P: Ca t, where / is the number of years after ffi{1},that describes the population of Europe.17. Sketch a graph of the exponential function f(x) :4-* by making a table of values.a) Table:b) Graph (mark the scale and the axes):1 8. In 1970 the US population was 203.3 million. By 2003 it had grown to 294 million.Let / be the number of years after 1970a). Find a linear function y: mt + b that models the data.b) Find an exponential function y: Calthat models the data. Round a to 3 decimalplaces.c) According to the latest census report (www.*ensLr$.$CI\dls#ffipsndialslatabi, the USpopulation in2012 is 312.8 million. Which of the above models gives a better estimate ofthe real data? Show work.MATH 111 F20r]SHOW ALL WORKTest Z(Ch.2-3)NO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK4 points each1. The following table shows the number of new AIDS cases reported in Florida from1986 to 1994.Year New AIDS Casesl0(55 -to3l= ///y, /qq3- 86Calculate the average annual rate of change of new AIDS cases per year from 1986 to1993. Round your answer to 2 decimal places, if necessary2. Find the average rate of change of the function y : 8 - 2x2 between x:0 andx:4.uvtvrX=o ? =9X = ,f of = , -2,Y L= 8-32 = - l?,'*Lc,-++ =-r=23. Use the graph below to find the average rate ofand x: 6 (1 cell: 1 unit).change of the function between x: 3t-v --L-7-- 4L'7', *'/v J --=--the table belowk{-c'([,/)4. Find a linear function whose valm2-6 -6Z--tf 2-3-/Lvb = -69861031987 16339882650989 34489904018991 5471992 5086993 10958994 8617ucs arc IIx-40 26f(x) 6 -6 -t2-24*(rt=4x-65'.In 2000 there were 39.8 million Americans without health insurance. This number hasincreased at an average rate of 1.7 million people per year.a) Write a formula that models the number of Americans without health insurance x yearsafter 2000.Uf2 3q.f + IZ Xb) Find the number of Americans without health insurance in20l2. X = / Zv = 3q.8 + [,7, lZ = 60, 2 rnn'/hbtld ---6. Find an equation of the line that passes through (5, 6) and (7, -3).ln= -3-6.=-+' ,/,5;-/-5 zy-6=-Lf,r(x^f) tf :W7 : y is directly proportional to x and y is 45.6 when ;r is 6.a) Find a formula to describe y as a function ofx. ? Uj = k4Y,= KV) q56=k'6 , K 6o y.==gxb) Use the formula to findy *K"n.-F 10.V .7. 6'lrt = +6-6 -:-8. Find an equation of the line that is pefuendicular to x+ 4y: 8 and passes through,-t,r).41 = {_ x/ =+-f xJ_n =/= / x ttl'/-=/t-lXt-/29. You invested $7000 in two funds p-aying 6Yo andSYo annual interest, respectively. Atthe end of the year the total interest from these investments was $520. How much wasToPo ^20aa = S@oa0 06K + o,zf(7ooo-x)=52en'n6Y+f6o:o,o8/ =520/ zaao c6 rcoo ,'COO c'tt//L'h|/ . .* 6%a* P;4/.06 x +A r v3Pv-(2,o2 X =^:?0i0. The length ", ^{"Ad((*cer field is twice as long as it is wide. If the perimeterof the field is 300yards, what are its dimensions?wiliil =r/invested at eachrate?/ =t'Kt/nld a-{- 6'/aTooo'Y = lrt rrcs#/'a/- 8;ty, ^' .= 1,,(x+sr)Ar+!'/x =Jno6x.Pd,[= 52 /r( =/90'&^7tt = //(fu'orrs ious ; 50 X /oe Y"-aA11. In 2010 there were 13,000 students at college A, with a projected ernollment increaseof 1000 students per year. In the same year there were 16,500 students at college B, witha projected enrollment increase of 500 students per year.a) Find the functions rnodeling college enrollment for each college, let x be the number ofyears after 2010.College B:b) In what yearwill the colleges have the same enrollment?Collese