This week you were introduced to the natural number e 2.718. In mathematics there are several important numbers similar to e. You are likely familiar with the constant pi 3.14. For example: You are likely familiar with the constant pi 3.14. Do some research on either one of these two numbers, or, better yet, find another very important number in mathematics. Share with us what you have found out about the number, for example, its history, some trivial facts about the number, and/or how it is applied. QUESTION 1 Evaluate the function at the indicated value of x. Round your result to three decimal places. Function: f(x) = 0.5x Value: x = 1.7 -0.308 1.7 0.308 0.5 -1.7 5 points QUESTION 2 Match the graph with its exponential function. y = 2-x - 3 y = -2x + 3 y = 2x + 3 y = 2x - 3 y = -2x - 3 5 points QUESTION 3 Select the graph of the function. f(x) = 5x-1 5 points QUESTION 4 Evaluate the function at the indicated value of x. Round your result to three decimal places. Function: f(x) = 500e0.05x Value: x=17 1169.823 1369.823 1569.823 1269.823 1469.823 5 points QUESTION 5 Use the One-to-One property to solve the equation for x. e3x+5 = 36 x = -1/3 x2 = 6 x = -3 x = 1/3 x=3 5 points QUESTION 6 Write the logarithmic equation in exponential form. log8 64 = 2 648 = 2 82 = 16 82 = 88 82 = 64 864 = 2 5 points QUESTION 7 Write the logarithmic equation in exponential form. log7 343 = 3 7343 = 2 73 = 77 73 = 343 73 = 14 3437 = 2 5 points QUESTION 8 Write the exponential equation in logarithmic form. 43 = 64 log64 4 = 3 log4 64 = 3 log4 64 = -3 log4 3 = 64 log4 64 = 1/3 5 points QUESTION 9 Use the properties of logarithms to simplify the expression. log20 209 0 - 1/ 9 1 /9 -9 9 5 points QUESTION 10 Use the One-to-One property to solve the equation for x. log2(x+4) = log2 20 19 17 18 16 20 5 points QUESTION 11 Find the exact value of the logarithmic expression. log6 36 2 6 36 -2 none of these 5 points QUESTION 12 Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) log3 9x log3 9 x log3 x log3 9 + log3 x log3 9 log3 none of these 5 points QUESTION 13 Condense the expression to a logarithm of a single quantity. logx - 2logy + 3logz 5 points QUESTION 14 Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. log4 9 1.585 5.585 3.585 4.585 2.585 5 points QUESTION 15 Determine whether the given x-value is a solution (or an approximate solution) of the equation. 42x-7 = 16 x=5 no ye s 5 points QUESTION 16 Solve for x. 3x = 81 7 3 4 -4 -3 5 points QUESTION 17 Solve the exponential equation algebraically. Approximate the resulte to three decimal places. e5x = ex2-14 -7, -2 7, -2 5, -14 7, 2 -7, 2 5 points QUESTION 18 Solve the logarithmic equation algebraically. Approximate the result to three decimal places. log3(6x-8) = log3(5x + 10) 18 20 17 19 -2 5 points QUESTION 19 Find the magnitude R of each earthquake of intensity I (let I0=1). I = 19000 3.28 5.28 4.28 2.38 6.28 5 points QUESTION 20 $2500 is invested in an account at interest rate r, compounded continuously. Find the time required for the amount to double. (Approximate the result to two decimal places.) r = 0.0570 13.16 years 10.16 years 11.16 years 12.16 years 14.16 years 5 points 1. Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function. Rises to the left, falls to the right Rises to the right, rises to the left Falls to the left, rises to the right Falls to the right Falls to the left, falls to the right 4 points QUESTION 2 Select the correct description of right-hand and left-hand behavior of the graph of the polynomial funciton. f(x) = 4x2 - 5x + 4 Falls to the left, rises to the right Falls to the left, falls to the right Rises to the left, rises to the right Rises to the left, falls to the right Falls to the left 4 points QUESTION 3 Find all the real zeroes of the polynomial function. f(x) = x2 - 25 -25 5 -5 25 5 4 points QUESTION 4 Use synthetic division to divide. (4x3 + x2 - 11x + 6) (x + 2) 4x2 - 5x - 6 4x2 - 7x + 3 4x2 - 2x - 2 4x2 + 5x - 12 4x2 + 7x - 4 4 points QUESTION 5 Use the Remainder Theorem and synthetic division to find the function value. Verify your answers using another method. h(x) = x3 - 6x2 - 5x + 7 h(-8) -849 -847 -851 -848 -845 4 points QUESTION 6 Find all the rational zeroes of the function. x3 - 12x2 + 41x - 42 -2, -3, -7 2, 3, 7 2, -3, 7 -2, 3, 7 -2, 3, -7 4 points QUESTION 7 The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by R(p) = -25p2 + 1700p where p is the price per unit (in dollars). Find the unit price that will yield a maximum revenue. $38 $35 $36 $37 $34 4 points QUESTION 8 Find the domain of the function Domain: all real numbers x except x = 7 Domain: all real numbers x except x = 49 Domain: all real numbers x except x = 8 Domain: all real numbers x except x = -7 Domain: all real numbers x except x = 7 4 points QUESTION 9 Find the domain of the function and identify any vertical and horizontal asymptotes. Domain: all real numbers x Vertical asymptote: x = 0 Horizontal asymptote: y = 0 Domain: all real numbers x except x = 2 Vertical asymptote: x = 0 Horizontal asymptote: y = 0 Domain: all real numbers x except x = 5 Vertical asymptote: x = 0 Horizontal asymptote: y = 2 Domain: all real numbers x Vertical asymptote: x = 0 Horizontal asymptote: y = 2 Domain: all real numbers x except x = 5 Vertical asymptote: x = 5 Horizontal asymptote: y = 0 4 points QUESTION 10 Simplify f and find any vertical asymptotes of f. x+3; vertical asymptote: x = -3 x; vertical asymptote: none x; vertical asymptote: x = -3 x-3; vertical asymptote: none x2; vertical asymptote: none 4 points QUESTION 11 Determine the equations of any horizontal and vertical asymptotes of horizontal: y = 5; vertical: x = 0 horizontal: y = 1; vertical: x = -5 horizontal: y = 1; vertical: x = 1 and x = -5 horizontal: y = -1; vertical: x = -5 horizontal: y = 0; vertical: none 4 points QUESTION 12 Identify all intercepts of the following function. x-intercepts: (3, 0) no intercepts x-intercepts: (-3,0) x-intercepts: (0,0) x-intercepts: (3,0) 4 points QUESTION 13 Select the correct graph of the function. 4 points QUESTION 14 The game commission introduces 100 deer into newly acquired state game lands. The population N of the herd is modeled by where t is the time in years. Find the populations when t=40. (Round your answer to the nearest whole number.) 1,442 deer 1,632 deer 1,594 deer 1,550 deer 1,500 deer 4 points QUESTION 15 Evaluate the function at the indicated value of x. Round your result to three decimal places. Function: f(x) = 6000(6x) Value: x = -1.3 584.191 784.191 -584.191 684.191 -784.191 4 points QUESTION 16 Select the graph of the function. 4 points QUESTION 17 Use the One-to-One Property to solve the equation for x. ex2-6 = e5x x = -6 x=5 x = 6, -1 x = -6, -1 x = -6,1 4 points QUESTION 18 log366 = 1/2 36 = -6 36 = 6 6 = 36 36 = -1/6 36 = 1/6 4 points QUESTION 19 Write the exponential equation in logarithmic form. 272 = 729 log27729 = 2 log27729 = 1/2 log72927 = 2 log27729 = -2 log272 = 729 4 points QUESTION 20 Find the exact value of the logarighmic expression without using a calculator. 4 ln e7 7 28 4 e 1 4 points QUESTION 21 Condense the expression to the logarithm of a single quantity. ln310 + ln3x ln3(10 - x) ln310/x ln3(10 + x) ln310x ln310x 4 points QUESTION 22 Solve for x. 6x = 1,296 6 10 4 -6 -4 4 points QUESTION 23 Solve the exponential equation algebraically. Approximate the result to three decimal places. ex - 8 = 12 ln20 2.485 ln20 2.996 ln20 -2.485 ln20 2.079 ln20 -2.996 4 points QUESTION 24 An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment? 1 year 14.40 years 13.86 years 14.86 years 13.40 years 4 points QUESTION 25 The populations (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modele by where t represents the year, with t = 0 corresponding to 2000. Use the model to find the population in the year 2001. 2,418,774 2,419,774 2,421,774 2,420,774 2,422,774 4 points