Math 148 Exam 2 Practice Problems 1) Solve a) Find the value of x (without using logarithms) that makes the statement true: xx 84 9 = + b) Solve the equation: 10)20log( 5 =−x . 2) Express as a single logarithm. a) () x xx log 3 log 2 − + b) ()ln( 1) 2 ln 5 lnx xx−− ++⎡⎤ ⎣⎦ 3) Kevin wishes to deposit $3000 for a period of 2 years so he can travel and vacation in the future. He can choose between 4 plans: a) 6.5% interest compounded continuously b) 6.55% interest compounded monthly c) 6.6% interest compounded quarterly d) 6.65% interest compounded annually i) Which plan will return the most money? ii) Suppose he invested $1500 in the 6.5% account and the other $1500 in the 6.6% account, compute the total amount of interest he would earn at the end of 2 years. 4) Assume that f(t) is an exponential function with f(0) = 200 and f(3) = 2000. a) Use the form rt Petf =)( to find the equation of this exponential function. b) When the function f is expressed in the form x Paxf =)( , the constant a is called the growth factor. Find the growth factor of the function f. c) What input value will give you an output value of 5000? 5) The function .0479 () 1 t gt e − =− gives the percentage of the population (expressed as a decimal) that has seen a new TV show t weeks after it has gone on the air. a) What percentage of people have seen the show after 24 weeks? b) Approximately when will 90% of the people seen it? 6) Darlene wants to have $30,000 available in five years from now for a down payment on a house. She has inherited $25,000. How much of the inheritance should be invested at 5.7% annual interest, compounded quarterly, to accumulate the $30,000. 7) The following table gives the value of a car purchased for $21,000 after t years of ownership: Age of Car Value 0 21,000 6 7,000 12 2333.33 Assume that P is the price of the car after t years. Which of the following equations would be a good model for the values in the table above? i) t tP )3(000,21)( = ii) t tP ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 3 1 21000)( iii) 6 3 1 21000)( t tP ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = iv) 6 )3(000,21)( t tP = 8) Answer each of the statements below as True or False. If false, make it true. a) For any real number x, xe x =ln . b) 10lnln 10ln ln2 2 −= x x for all positive x. c) )3log(1)30log( xx += for all positive x. d) )2ln()ln()2ln( +=+ xx for all positive x. 9) A computer software company claims the following function models the “learning curve” for their mathematical software. t e tP 52.0 2.481 100 )( − + = Where t is measured in months and P(t) is the average percent of the software program’s capabilities mastered after t months. a) Initially, what percent of the program is mastered? b) After six months, what percent of the program is mastered? c) If the company’s claim is true, how many months will it take to have mastered 80 percent of the program? d) According to the model, what would be a reasonable number of months for someone to have mastered nearly 100 percent of the program’s features? 10) Solve a) Solve the equation )3415ln()ln(2 += xx b) Write the exact solution, which must include logarithms, to the equation 1 2 + = xx e c) Using my calculator, I found the solution to the equation 6029 4 = − x e to be approximately -0.1817622. Write the exact solution to the equation. (YOUR ANSWER MUST INCLUDE LOGARITHMS.) 11) Express the following uncertainty intervals using ± notation. a) (2.45, 4.9) b) (5.12, 6.26) 12) Find the area of the trapezoid with h = 2.340 cm, a = 1.15 cm and b = 3.2 cm. Round your answer to the least significant position. 1 () 2 Ahab=+ 13) a) If H varies directly as T, then H · T is a constant. True False b) If two quantities vary inversely, when one is halved the other i) doubles ii) quadruples iii) stays unchanged iv) is halved c) V varies directly as the cube of r. If V = 33.5 when r = 2, then the constant of proportionality is i) 268 ii) 8.375 iii) 4.1875 iv) 16.75 14) Find the central angle θ of a circular sector if the arc that it subtends is 4 9 of the circumference. 15) In a circle that has area of 41π cm 2 , find the central angle and the arclength of a circular sector with area 42.935 cm 2 . Give your answers accurate to 4 significant positions. george Microsoft Word - 148exam2