MTH 112 Practice Problems for Test 3

Transcription

1 MTH 112 Practice Problems for Test 3 Solve the polnomial inequalit and graph the solution set on a number line. Epress the solution set in interval notation. 1) (- 2)( + ) > 0 1) ) ) ) ( + 2)( - 1)( - 6) > 0 3) Solve the rational inequalit and graph the solution set on a real number line. Epress the solution set in interval notation. ) < 0 ) ) ( - 1)(3 - ) ( - 2)2 0 ) Solve the inequalit. 12 6) - > + 1 6) Solve the problem. 7) If varies directl as the square of, and = 0 when = 8, find when = 20. 7) 8) If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit is directl proportional to the amount of voltage applied to the circuit. When 3 volts are applied to a circuit, 7 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 11 volts. 8) 9) varies inversel as 2, and = when = 12. Find when =. 9) 1

2 Solve. ) If the voltage, V, in an electric circuit is held constant, the current, I, is inversel proportional to the resistance, R. If the current is 90 milliamperes when the resistance is ohms, find the current when the resistance is 12 ohms. ) Write an equation that epresses the relationship. Use k for the constant of proportionalit. 11) q varies jointl as r and s and inversel as the square root of a. 11) Write an equation that epresses the relationship. Use k as the constant of variation. 12) The weight of a bod above the surface of the earth is inversel proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied b? 12) Find the variation equation for the variation statement. 13) c varies directl as a and inversel as b; c = when a = 8 and b = 8 13) Solve the problem. 1) f varies jointl as q2 and h, and f = 6 when q = and h = 2. Find f when q = 3 and h =. 1) 1) The amount of paint needed to cover the walls of a room varies jointl as the perimeter of the room and the height of the wall. If a room with a perimeter of 70 feet and 8-foot walls requires.6 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of feet and 6-foot walls. 1) Approimate the number using a calculator. Round our answer to three decimal places. 16) 2. 16) Solve the problem. 17) A cit is growing at the rate of 0.6% annuall. If there were,80,000 residents in the cit in 1993, find how man (to the nearest ten-thousand) are living in that cit in Use =,80,000(2.7)0.006t. 17) Graph the function b making a table of coordinates. 18) f() = 3 18)

3 The graph of an eponential function is given. Select the function for the graph from the functions listed. 19) 19) A) f() = - 1 B) f() = - 1 C)f() = D) f() = + 1 Approimate the number using a calculator. Round our answer to three decimal places. 20) e1.6 20) Solve the problem. 21) The size of the bear population at a national park increases at the rate of.2% per ear. If the size of the current population is 138, find how man bears there should be in 3 ears. Use the function f() = 138e0.02t and round to the nearest whole number. 21) Use the compound interest formulas A = P1 + r n nt and A = Pe rt to solve. 22) Find the accumulated value of an investment of $800 at % compounded quarterl for ears. 22) 23) Find the accumulated value of an investment of $7000 at 7% compounded continuousl for 6 ears. 23) Write the equation in its equivalent eponential form. 2) log 3 9 = 2 2) 2) log b 23 = 2) Write the equation in its equivalent logarithmic form. 26) 63 = 26) 27) = 00 27) Evaluate the epression without using a calculator. 28) log ) 29) log ) 3

4 30) log ) 31) 6 log ) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 32) log 6 (7 11) 32) 33) log (12) 33) 3) log 3 7 3) 3) log,000 3) 36) logn 8 36) 37) ln 9 37) 38) log b (z) 38) 39) log ) 0) log 2 0) 1) log c + log c 1) 2) log ( + 7) - log ( - 3) 2) 3) ln + 8ln 3) ) 3log 6 + log 6 ( - 6) ) Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places ) log 28 ) 6) log )

5 Solve the equation b epressing each side as a power of the same base and then equating eponents. 7) 3(6-3) = ) 8) = 6-8) Solve the eponential equation. Epress the solution set in terms of natural logarithms. 9) 8 3 = 2.3 9) 0) e3 = 6 0) Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 1) = 3 1) 2) e2-8 - = 121 2) Solve the logarithmic equation. Be sure to reject an value that is not in the domain of the original logarithmic epressions. Give the eact answer. 3) log 3 = 3) ) ln = 2 ) ) log 3 + log 3 = 1 ) 6) log 3 ( + 6) + log 3 ( - 6) - log 3 = 2 6) 7) log ( + ) = 3 + log ( + 1) 7) 8) log = log + log ( - 3) 8) Solve. 9) The value of a particular investment follows a pattern of eponential growth. In the ear 2000, ou invested mone in a mone market account. The value of our investment t ears after 2000 is given b the eponential growth model A = 3300e0.03t. How much did ou initiall invest in the account? 9) 60) The population of a particular countr was 29 million in 1980; in 1989, it was 3 million. The eponential growth function A =29ekt describes the population of this countr t ears after Use the fact that 9 ears after 1980 the population increased b 6 million to find k to three decimal places. 60)

6 REVIEW FROM PREVIOUS MATERIAL Find and simplif the difference quotient f( + h) - f(), h 0 for the given function. h 61) f() = 2 61) Evaluate the piecewise function at the given value of the independent variable. 62) h() = if = 7 if 7 ; h(7) 62) Graph the function. + if -8 < 2 63) f() = - if = if > 2 63) Begin b graphing the standard square root function f() =. Then use transformations of this graph to graph the given function. 6) g() = ) Find the inverse of the one-to-one function. 6) f() = 7-8 6) 6

7 Find the domain of the function. 66) f() = 6-66) For the given functions f and g, find the indicated composition. 67) f() = -, g() = + (g f)() 67) Find a rational zero of the polnomial function and use it to find all the zeros of the function. 68) f() = ) Solve the polnomial equation. In order to obtain the first root, use snthetic division to test the possible rational roots. 69) = 0 69) Find an nth degree polnomial function with real coefficients satisfing the given conditions. 70) n = ; 3, 1, and 1 + 2i are zeros; f(1) = 8 70) 3 7

8 Answer Ke Testname: TEST 3 PRACTICE PROBLEMS SPR 11 1) (-, -) (2, ) ) [-, 6] ) (-2, 1) (6, ) ) (-2, 8) ) (-, 1] [3, ) ) (-31, -1) or (, ) 7) 20 8) 27 milliamperes 9) = 36 ) 30 milliamperes 11) q = krs a 12) The weight is divided b 16 13) c = a b 1) f = 72 1) 2.7 quarts 16) ),00,000 18) ) C 20).93 21)

9 Answer Ke Testname: TEST 3 PRACTICE PROBLEMS SPR 11 22) $ ) $, ) 32 = 9 2) b = 23 26) log 6 = 3 27) log 00 = 28) 3 29) -3 30) 0 31) 17 32) log log ) 3 + log 3) log log 3 3) log - 36) 8logn 37) 1 9 ln 38) log b + log b z 39) 3log 3-8log 3 0) 1 2 log 2-2 1) log c () 2) log ) ln 8 ) log 6 3( - 6) ) ) ) {3} 8) 33 ln 2.3 9) 3 ln 8 0) ln 6 3 1) -.2 2) 7.6 3) {23} ) e2 ) { 3 } 6) {12} 7) ) {1} 9) $

10 Answer Ke Testname: TEST 3 PRACTICE PROBLEMS SPR 11 60) ) (2+h) 62) -1 63) (2, 7) (2, 3) - - (-8, -3) - (2, -) - 6) ) f-1() = ) (-, 6] 67) 68) - 1 2, 2, 3 69) - 1, 2, 70) f() =