Math 095 Final Exam Review - Faculty.chemeketa.edu

Math 095 Final Exam Review - MLCAlthough this is a comprehensive review, you should also look over your old reviews from previousmodules, the readings, and your notes. Round to the thousandth unless indicated otherwise.Module I – Sections 1.1, 1.6, 2.1, 2.2, 2.3, 4.1, and 4.21. Consider the graph of the function, f at the right.a) How can you tell thatthe graph represents afunction?b) What is theindependentvariable?c) What is the dependentvariable?d) What is the value of f( 6 )? f(-2)?e) For what values of x isf (x) = 2f) What is the domain ofthe function?g) What is the range ofthe function?2. Do the tables represent functions? How do you know?a) b)3. The graph at right represents a scattergram and a linear model for the number of companies on the Nasdaqstock market between 1990 and 1999, where n represents the number of companies t years after 1990.a) Using the linear model, in what year werethere approximately 3500 companies?b) What is the n-intercept of the linear model andwhat does it mean?c) What is the t-intercept and what does it mean?d) From the linear model, what would youpredict the number of companies to be in theyear 1996?4. Find a linear equation of the line that passes through the given pairs of points.a) (3, 5) and (7,1) b) (−4, −6) and (−2, 0)5. The average consumption of sugar in the U.S. increased from 26 pounds per person in 1986 to 136 pounds perperson in 2006. Let p be the average number of pounds consumed t years after 1980. Find an equation of alinear model that describes the data.

6. If f (x) = 2x 2 + 4 , find the following. a) b) c)Module II – Sections 4.3, 4.4, 4.5, 5.2, 5.3, 5.4, and 5.67. Simplify each of the following and write without negative exponents.y 3 −2⎛ ⎞a)⎝⎜ 4 ⎠⎟b) 6x2 y −3x −1 y 4 c) 5x −2 2x 5 + x 2( ) d)10p −48. Simplify each expression using the laws of exponents. Write the answers with positive exponents.4x( ) 3x 4 3( ) 3 4b)a) −5x 2 35x⎛c)⎝⎜m 2t 3⎞⎠⎟− 3 512( )d) m 6 n 49. Leta) What is the y-intercept of the graph of f? b) Does f represent growth or decay?c) Find f(-2) d) Find f(2) e) Find x when f (x) = 3210. Find an approximate equation of the exponential curve that contains the given set of points. (0, 7)and (3, 2).11. Sue invested $4000 in an account that pays 6% interest compounded annually. Let f(t) represent the value ofthe account after t years. a) Write an equation for f. b) What is the account worth after 12 years?12. Find the value of each logarithm. a) log 6(36) b) ln(e 12 )13. Rewrite the log equations in exponential form. a) log bt = k b) ln p = m14. Rewrite the exponential equations in log form. a) b) c)15. Solve each of the equations.a) 3(4) x−2 = 15 b) 3log(x + 2) = 9 c) 5ln(x − 3) = 4516. A population of 35 fruit flies triples every day. Let be the number of flies after t days.a) Write an equation for the function, f, that models the fruit fly population growth.b) How many fruit flies are there after 5 days?c) How long will it take for the fruit fly population to reach 25000?17. The population of Smalltown decreased from 1910 to 1960, as shown in the table at the right.Let p(t) be the population of Smalltown t years after 1910.a) Use exponential regression to find an equation for p. Round to two decimal places.b) What is the coefficient a in your model and what does it represent?c) Use your function to predict the year the population reaches 150.18. Use the intersect feature on a graphing calculator to solve the equation. 3ln(x + 5) = 5+ 2x

Module III – Sections 7.2, 7.3, 7.5, 7.7, and 7.819. Given the graph of the equation: y = 5x 2 − 3x − 2a) Which does the graph have, a maximum or a minimum?b) Calculate the coordinates of the vertex by hand and using the Minimum feature on a calculator.c) What is the y-intercept of the graph?d) What are the x-intercepts of the graph?20. Simplify the radical expressions: a) b)21. Solve each of the equations: a) b) (x + 2) 2 = −3c) x 2 − 7x = −12 d) x 2 − 6x + 9 = 0 e) −x 2 − 4 = 2x22. A football player kicks a ball. The height of the ball, h(t) in feet, t seconds after it is kicked, is given by theequation h(t) = −16t 2 + 60t + 5 .a) What is the height of the ball after 3 seconds?b) At what time/s is the ball 5 feet off the groundc) How long does it take the ball to hit the ground?23. The population of Iceland (in thousands) from 1950 to 2000 is given in the table atthe right.a) What kind of equation fits the data best, quadratic or exponential?b) Use quadratic regression to find a model for the data where f(t) is thepopulation t years after 1950.c) Predict the year that maximum population is reached.d) Predict the maximum population.e) In what years does model breakdown occur?1749c)Module IV – Sections 8.7, 10.1 and 10.224. Write an equation, then find the requested value of the variable.a) If t varies directly as the square of p, and t = 36 when p = 3, find t when p = 4.b) If M varies inversely as the square root of r, and M = 3 when r = 25, find M when r = 9.25. Using a nnotation, find a formula of each sequence.a) −7, −11, −15, −19, −23,... b) −7, −14, −28, −56, −112,...26. Find the 21 st term of the sequence: 67, 72, 77, 82, 87,...27. Find the term number n of the last term of the finite sequence: 1, 6, 11, 16, 21, ... 47128. Find the 67th term of the sequence. Write your answer in scientific notation if necessary.5, 15, 45, 135, 405,...29. −2,470,629 is a term of the sequence; −3, −21, −147, −1029, −7203,...Find the term number of that term.30. Find an equation of a function f such that f (1), f (2), f (3), f (4), f (5), ...is the sequence 7, 3, −1, −5, −9,...