Math 112 Practice Problems for Test #3

Transcription

1 Math Practice Problems for Test #3 These are problems designed to help ou prepare for Test #3. The are not necessaril test questions. You can also practice assigned homework problems from the tetbook, or in MMathLab. There might also be questions from Test and/or Test material. Determine whether the functions are inverses of each other. ) f() = - 3 g() = - 3 ) f() = ) f() = + g() = + Find the inverse of the one-to-one function. 3) f() = 8 + ) f() = ( + ) ) f() = Approimate the number using a calculator. Round our answer to three decimal places. ). 7) 3 -. The graph of an eponential function is given. Select the function for the graph from the functions listed. ) 0 8) ) e. Graph the function b making a table of coordinates. 0) f() = - -0 A) f() = - B) f() = - C) f() = + D) f() =

2 3) 0 8) Suppose that ou have $3000 to invest. Which investment ields the greater return over 8 ears: 7.% compounded monthl or 7.3% compounded quarterl? -0-0 Write the equation in its equivalent eponential form. 9) log = 3-0) log = 3-0 ) log b 9 = A) f() = 3 + B) f() = 3 C) f() = 3 - D) f() = 3 - Write the equation in its equivalent logarithmic form. ) 3 = ) 0 3) -3 = ) 3 33 = Evaluate the epression without using a calculator. ) log ) log 0 0,000 A) f() = - B) f() = C) f() = - D) f() = - - Use the compound interest formulas A = P + r nt and A n = Pe rt to solve. ) Find the accumulated value of an investment of $000 at 0% compounded annuall for 0 ears. 7) log 7 7 8) log 8 9) log 30) log ) Find the accumulated value of an investment of $,000 at % compounded semiannuall for ears. 7) Find the accumulated value of an investment of $7000 at 7% compounded continuousl for ears. 3) log 9 9 Evaluate or simplif the epression without using a calculator. 3) log ) log 00 3) log 0.000

3 3) log 0 3) ln e 3 0) log 3 37) ln e 38) Be sure to know the bacis graphs for Logarithmic functions. Where is the -intercept? What is the vertical asmptote? Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 39) log 3 (3) 0) log 9 ( + ) ) log 3 7 ) log 9 9 3) logn 8 ) ln 9 ) log 3 - Use properties of logarithms to condense the logarithmic epression. Write the epression as a single logarithm whose coefficient is. Where possible, evaluate logarithmic epressions. 3) log c + log c ) log ( + 7) - log ( - 3) ) 7 ln - 3 ln ) log 8 + log 8 7) 9ln ( - ) - ln 8) (log 7 (r - 9) - log7 r) ) log b (z ) ) log 7 3 ) log ) log 3 + 8) log 7 9) log 3 9-9) log3 + log 3 (r - ) - log 3 r 0) 3 (log + log ) Use the change of base formula and a calculator to evaluate to four decimal places ) log 8 ) log 38 3) log π 7 3

4 Solve the equation b epressing each side as a power of the same base and then equating eponents. Give the ʺEXACTʺ answer. ) = 80) log 3 ( - ) = 8) log + log ( - 3) = ) 3 ( + ) = 3 8) log 7 ( + ) - log 7 = ) 3 ( - 3) = 7 83) log 3 ( + ) + log 3 ( - ) - log 3 = 7) + 9 = - 8) e + 7 = e 0 Solve the eponential equation. Epress the solution set in terms of natural logarithms. Give the ʺEXACTʺ answer. 9) 8 3 =.3 70) = 7) e 3 = 7) + = + Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 73) 0 = 3.0 7) e = 3. 7) e = Solve. 8) The value of a particular investment follows a pattern of eponential growth. In the ear 000, ou invested mone in a mone market account. The value of our investment t ears after 000 is given b the eponential growth model A = 800e 0.0t. When will the account be worth $88? A) 00 B) 00 C) 003 D) 00 8) The population of a particular countr was million in 983; in 99, it was 3 million. The eponential growth function A =e kt describes the population of this countr t ears after 983. Use the fact that 8 ears after 983 the population increased b 0 million to find k to three decimal places. A) 0.07 B) 0.07 C) 0.88 D) ) A fossilized leaf contains 3% of its normal amount of carbon. How old is the fossil (to the nearest ear)? Use 00 ears as the half-life of carbon. A) 3,0 B) 3 C) 0,8 D),3 7) 7 = + 7 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. 77) log 3 = 78) log ( - 3) = - 79) log ( + ) + log ( - ) =

5 Answer Ke Testname: REVTEST3SUM0 ) g() and h() ) None 3) f - () = - 8 ) f - () = 3 - ) f - () = 3-8 ) ) 0.7 8).79 9).93 0) ) ) D 3) C ) C ) $0,3.00 ) $8,9. 7) $0,3.73 8) $3000 invested at 7.3% compounded quarterl over 8 ears ields the greater return. 9) 3 = 0) 3 = ) b = 9 ) log = 3

6 Answer Ke Testname: REVTEST3SUM0 3) log = -3 ) log 33 7 = 3 ) ) 7) 8) -3 9) - 30) 0 3) 3) 3 33) - 3) - 3) 3) 3 37) 38) -int: (, 0) V.A.: -ais or =0 39) + log 3 0) log + log ( + ) 9 9 ) log 7 - log 3 3 ) - log 9 3) 8logn ) log b + log b z ) log 7 + log - log 3 ) 3 log - 8 log 3 3 7) log ( + ) - log 3 3 8) log 7 + log 9) - log 3 ( - ) 0) 3 log + log - ) 9 ln ) log + log 3) log () c + 7 ) log - 3

7 Answer Ke Testname: REVTEST3SUM0 ) ln 7 3 ) log 8 7) ln 8) log7 ( - )9 r - 9 r 9) log3 3 r - r 0) log 3 ).037 ).88 3).70 ) {} ) {} ) {3} 7) 33 8) -7 ln.3 9) 3 ln 8 70) 7) 7) ln ln 3-8 ln 3 73) 0.9 7). 7) 0.9 7) ) {3} 3 78) 79) {7} 80) {3, -} 8) {3} 8) { } 83) {} 8) B 8) A 8) D ln - ln ln - ln 7