MATH 111 F2013 Practice Test 2b SHOWALL WORK NO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK 4 points each 1 The table shows the number of manatees killed by power boats in Florida from 1986 through 1996 Year 1986 1987 1988 1989 1990 Manatees killed 33 39 43 50 47 Find the average rate of change of the number of rurnatees killed annually from 1986 to 1990 2x x2 between x 2 andx 5 2 Find the average rate of change of the function y 3 Use the graph below to find the average rate of change of the function from x 2 to x 6 lcell lunit 4 Find a linear function whose values are given in the table below 6 3 0 x 8 6 5 f x 15 11 Find an equation of the line that passes through 2 I and 5 3 y is directly proportional to x andy is 17 4 when x is 6 a Find a fomrula to describe y as a function of x b Use the formula to findy when x is 8 8 Find an equation of the line that is perpendicular to 4x 8y I and passes through Q 5 9 You invested 9000 in trvo funds paying 4Yo and 7 o annral interest respectively At the end of the year the total interest from these invesfinents was 555 How much was 6 7 invested at each rate 10 The length of a rectangular field exceeds the widthby 260 yards If the perimeter of the field is 1000 yards what are its dimensions 11 At a price ofp dollars per ticket the number of tickets to a rock concert that can be sold is given by the demand model y 45p 7800 The number of tickets that the concert s promoters are willing to make available is given by the supply model Y 5P 6000 a How many tickets can be sold and supplied for 50 per ticket b Find the ticket price and the number of tickets supplied and sold at the equilibrium price 12 Find the equation x 1 0 1 2 f x Cd for the function given by the table below flx 3 4 26 6 05 8 59 Round values to 2 decimal places 13 A patient is administered 250 mg of a therapeutic drug It is known that40Yo of the drug is expelled from the body each hour a Find an exponential decay model for the amount of drug remaining in the patient s body after t hours b Use the model to predict the amount of drug remaining in the patient s body after 10 hours 14 For an exponentialfuncnon f x Cd where r is measured in months andf O 13 ndf g 48 find a the 9 month growth factor b the monthly growth factor Round answers to 2 decimal places 15 Find the accumulated value of an investnent of 5000 for 10 years at an interest rate of 6 SYo compounded a semiannually b monthly 16 In 2000 the population of Israel was approximately 6 04 million and by 2050 it is projected to grow to l0 million Use the exponential growth model P Ca where I is the number of years after 2000 to find an exponential growth function that models the data 16 In 2000 the population of Israel was approximately 6 04 million and by 2050 it is projected to grow to 10 million Use the exponential growttr model P Ca t where is the number of years after 2000 to find an exponential growth function that models the data 17 Sketch a graph of the exponential functions in the same coordinate plane by making a table of values f x 3 and g x 3 ANSWERS 1 3 5 2 5 3 0 25 4 y 5 V l 3 x 6 1155 165x 6 y 13 x lll3 7 a y 2 9x b 23 2 8 Y 2x 9 9 2500 at4Yo and 6500 atTVo 10 120x380 ll a 6250 supplied 6550 sold b p 60 per ticket 6300 tickets 12 f x 4 26 1 42 13 a A 250 0 6 t b 1 51 mg t4 a 3 69 b 1 16 15 a 9479 te b 9560 92 16 t7 x P 6 04 1 01 t 1 0 I 2 X J t 3 I 3 9 x 2 9 t 0 J 1 I t 3 J X