Math 1101 Exam 3 Practice Problems

Transcription

1 Math 0 Exam 3 Practice Problems These problems are not intended to cover all possible test topics. These problems should serve as an activity in preparing for your test, but other study is required to fully prepare. These problems contain some multiple choice questions, please consult with your instructor for particular details about your class test.. Decide whether or not the functions are inverses of each other. f(x) = 5 4x + 5, g(x) = x + 4 x 2. Determine whether or not the function is one-to-one. (a) A. Yes B. No (b) f(x) = 8x 2 3 A. Yes B. No 3. Determine whether the function that pairs students ID numbers with their GPAs is an invertible function. A. Yes B. No 4. Find the inverse of the function f(x) = 5x 2 2x 8 5. Graph the function using transformations of an exponential function s graph with which you are familiar f(x) = 4 x 2 + 3

2 MATH 0 Exam 3 Review, Page 2 of 6 Fall A computer is purchased for $4800. Its value each year is about 78% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function V (t) = 4800(0.78) t. Find the value of the computer after 7 years. 7. What are the domain and range for the equation y = 2 x? A. Domain: (0, ); Range (, ) B. Domain: (, ); Range (0, ) C. Domain: (, ); Range (, ) D. Domain: (, ); Range [0, ) 8. Write the logarithmic equation in exponential form. (a) log 5 25 = 3 (b) ln x = 7 A. x = e 7 B. x = ln 7 C. No solution D. x = e 7 9. Find the value of without using a calculator. A. 6 B. 2 C. 2 D. 6 log Graph the function f(x) = log 2 (x) Find the inverse of the function f(x) = 8 x. A. f (x) = log x 8 B. f (x) = ln 8x C. f (x) = log 8 x D. f (x) = x 8 2. Solve the equation log 5 x = 2 A. 3 B. C. 0 D A certain noise( has an intensity I of Give that decibel level L is related to intensity I by L = 0 log I 0 ), where I 0 = 0 2, determine the decibel level of the noise. Round your answer to the nearest decibel. A. 69 decibels B. 82 decibels C. 79 decibels D. 8 decibels 4. Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. log 6 3 y 2 x

3 MATH 0 Exam 3 Review, Page 3 of 6 Fall Rewrite as a single logarithm. 2 log 2 x log 2 x 4 6 log 2 x A. log 2 x 7/6 B. log 2 x 9/2 C. 7 6 log 2 x 8 D. log 2 x 7 6. Solve the equation by hand. Give the exact answer and then an approximation rounded to the nearest thousandth. 5 5x = Solve the equation. Give an exact solution. A. 5 B. 5, 2 C. 5 D. 2, 5 log(x 3) = log x 8. The sales of a new model of notebook computer are approximated by S(x) = e x/9, where x represents the number of months the computer has been on the market, and S represents the sales in thousands of dollars. In how many months will the sales reach $5,000? 9. Assume the cost of a car is $27,000. With continuous compounding in effect, the cost of the car will increase according to the equation C = 27000e rt, where r is the annual inflation rate and t is the number of years. Find the number of years it would take to double the cost of the car at an annual inflation rate of 5.2%. Round the answer to the nearest hundredth. A years B..96 years C years D years 20. Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. A. f(x) = (.09)(527.34) x B. f(x) = (567.57)(0.7) x C. f(x) = (527.34)(.09) x D. f(x) = (0.7)(567.57) x x y Find the exponential function which models a solid with initial mass of 22 grams, decreasing at a rate of 3.% per day. 22. Find an exponential function that models the data below and use it to predict about how many books will have been read in the eighth grade.

4 MATH 0 Exam 3 Review, Page 4 of 6 Fall 203 A. 330 B C. 883 D. 788 Grade Number of Books Read Several years ago, a large city undertook a major effort to encourage carpooling in order to reduce traffic congestion. The accompanying table shows the number of carpoolers, in thousands, from 995 to Use regression to obtain a function f(x) = a + b ln x that models the data, where x = corresponds to 995, x = 2 to 996, and so on. Round the constants a and b to the nearest hundredth. Year Carpoolers A. f(x) = ln x B. f(x) = ln x C. f(x) = ln x D. f(x) = ln x 24. Select an appropriate type of modeling function for the data shown in the graph. y A. Linear B. Cubic C. Exponential 25. Does it appear that a linear model or an exponential model is the better fit for the data given in the table below? x y x

5 MATH 0 Exam 3 Review, Page 5 of 6 Fall Jorge invested $2500 at 4% interest compounded semi-annually. In how many years will Jorge s investment have tripled? Round your answer to the nearest tenth of a year. 27. State the degree of the polynomial and whether the leading coefficient is positive or negative. A. 4: Leading coefficient is negative. B. 5: Leading coefficient is negative. C. 4: Leading coefficient is positive. D. 5: Leading coefficient is positive. 28. State the degree and leading coefficient of the polynomial f(x) = 2(x + 9) 2 (x 9) 2 A. Degree 4; leading coefficient B. Degree 4; leading coefficient 2 C. Degree 2; leading coefficient 2 D. Degree 2; leading coefficient 29. Predict the end behavior of the graph of the function f(x) =.48x 4 x 3 + x 2 8x + 4 A. Down on both sides B. Up on both sides C. Up on left side, down on right side D. Down on left side, up on right side

6 MATH 0 Exam 3 Review, Page 6 of 6 Fall P (x) = x x2 60x + 00, x 5 is an approximation to the total profit (in thousands of dollars) from the sale of x hundred thousand tires. Find the number of tires that must be sold to maximize profit. A. 5.5 hundred thousand B. 4 hundred thousand C. 5 hundred thousand D. 4.5 hundred thousand 3. Approximate the coordinates of each turning point accurate to two decimal places y = x 4 4x 3 + 4x The table below gives the number of births, in thousands, to females over the age of 35 for a particular state every two years from 970 to 986 Year Births (thousands) Use technology to find the quartic function that is the best fit for this data, where x is the number of years after 970. According to the model, how many births were to females over the age of 35 in this state in 990? A. 08,868 B. 06,368 C. 0,38 D. 94,368