Math 370 Exam 2 Review Name

Transcription

1 Math 70 Exam 2 Review Name Be sure to complete these problems before the review session. 10 of these questions will count as a quiz in Learning Catalytics. Round 1 will be individual. Round 2 will be in groups. Each round will account for half of your quiz grade. 1) Let g(x) = 5 x (a) Find the equation for g -1 (x). (b) Graph both g(x) and its inverse below. (a) (a) g -1 =log5(x+)+2 (b) Objective: (.1) Graph Exponential Functions 2) Suppose a substance has a half-life of 100 years. (a) If there is currently 50 grams of the substance, find an equation of the form A = A0e kt that gives the amount remaining after t years. (b) How long ago (to the nearest 0.1 year) were there 80 grams of the substance? (a) A = 50e t (b) 67.8 years ago Objective: (.1) Evaluate Functions with Base e ) Find the accumulated value of an investment of $100 at 8% compounded quarterly for 2 years. $ Objective: (.1) Use Compound Interest Formulas )

2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) log ) A) 1 B) 9 C) 22 D) log 9 1 A Objective: (.2) Use Basic Logarithmic Properties 5) Use properties of logarithms to expand log 7 4 m n 1 4 log 7 m + 1 log 7 n - 2 log 7 k Objective: (.) Expand Logarithmic Expressions k 2. 5) 6) Solve for x: 16 x + 4 = 64 x ) {8} Objective: (.4) Use Like Bases to Solve Exponential Equations 7) Solve for x: e 4x - e 2x - 28 = 0 (Give exact solutions.) 7) 1 2 ln(7) Objective: (.4) Use Logarithms to Solve Exponential Equations Solve the logarithmic equation. Give the exact answer. 8) log 2 (x + 1) + log 2 (x - 5) = 4 8) {7} Objective: (.4) Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the problem. 9) A couple wants to save for college for their newborn. If they will need $100,000 in 18 years, how much should they invest now if their investment will earn 6% interest, compounded continuously? $,960 Objective: (.4) Solve Applied Problems Involving Exponential and Logarithmic Equations 9) 10) Express the function y = 700(9) x with base-e instead of base 9. 10) y = 700e x ln 9, y = 700e 2.197x Objective: (.5) Express an Exponential Model in Base e

3 11) (a) Draw a unit circle and show the terminal side of an angle (in standard position) of 2 radians. (b) Convert the angle from part (a) to degrees. (b) (c) Give the exact values of all 6 trigonometric functions of the angle 2 (no calculator). sin 2 = cos 2 = tan 2 = csc 2 = sec 2 = cot 2 = (a) (c) sin 2 = - 2 Objective: (4.1) Use Radian Measure ; cos 2 (b) 1980 degrees = 1 2 ; tan = - ; csc 2 2 = ; sec = 2 cot 2 = - 12) If t is in Quadrant I, and cos t =, find sin t. 12) Objective: (4.2) Recognize and Use Fundamental Identities Use an identity to find the value of the expression. Do not use a calculator. 1) csc 2 - cot2 1) 1 Objective: (4.2) Recognize and Use Fundamental Identities Use a calculator to find the value of the trigonometric function to three decimal places. 14) cot -1 14).22 Objective: (4.2) Evaluate Trigonometric Functions with a Calculator

4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 15) A straight trail with a uniform inclination of 16 leads from a lodge at an elevation of 500 feet to a mountain lake at an elevation of 800 feet. What is the length of the trail (to the nearest foot)? A) 8114 feet B) 0,112 feet C) 28,298 feet D) 864 feet C Objective: (4.) Use Right Triangle Trigonometry to Solve Applied Problems 15) Determine the phase shift of the function. 16) y = -5 sin 4x ) 8 units to the right Objective: (4.5) Graph Variations of y = sin x 17) Graph the function given by y = - -2 sin x. 17) Objective: (4.5) Additional Concepts

5 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the function to its graph. 18) y = tan x ) A) B) C) D) A Objective: (4.6) Understand the Graph of y = tan x

6 Free Response. Show work for credit. 19) Graph y = 2 csc x. Be sure to show asymptotes and local extrema (min/max). 19) Objective: (4.6) Graph Variations of y = csc x and y = sec x Find the exact value of the expression. 20) csc ) Objective: (4.7) Understand and Use the Inverse Sine Function 21) cot -1 (-1) 21) 4 Objective: (4.7) Understand and Use the Inverse Cosine Function 22) sec -1 (1) 22) 0 Objective: (4.7) Understand and Use the Inverse Tangent Function Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 2) log (x + 6) + log (x - 6) - log x = 2 2) {12} Objective: (.4) Use the Definition of a Logarithm to Solve Logarithmic Equations

7 Graph the function. 24) y = -2 tan x 4 24) Objective: (4.6) Graph Variations of y = tan x MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a sketch to find the exact value of the expression. 25) sec tan -1 A) 2 B) 1 2 C) D) 2 D Objective: (4.7) Find Exact Values of Composite Functions with Inverse Trigonometric Functions 25) 26) A pie out of the oven cools according to the equation of the form ab t + c. The pie came out of the oven at 50 F, but you're not sure when. You measured the temperature twice. It was 120 F at 7 P.M., and 100 F at 7:0 P.M. If room temperature is 68 F, what time did the pie come out of the oven? About 1:44 before 7 PM, which is about 5:16 PM Objective:

8 27) Determine the equation of the function whose graph is shown. y = 2cos(x) - Objective: