NOTE: You must show your work to receive full credit. Simply stating the answer will not suffice.

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Gervais Perry
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1 MATH 1314 Review #3 Name NOTE: You must show your work to receive full credit. Simply stating the answer will not suffice. Graph the function by making a table of coordinates. 1) f() = 4 6 y 1) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of an eponential function is given. Select the function for the graph from the functions listed. 2) 10 y 2) A) f() = B) f() = C)f() = 5 D) f() = 5-1 1

2 NOTE: You must show your work to receive full credit. Simply stating the answer will not suffice. Graph the function. 3) Use the graph of f() = 5 to obtain the graph of g() = ) 6 y Solve the problem. 4) The function D(h) = 9e-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 8 hours? 4) Use the compound interest formulas A = P1 + r n nt and A = Pe rt to solve. 5) Find the accumulated value of an investment of $19,000 at 12% compounded annually for 13 years. 5) Write the equation in its equivalent eponential form. 6) log 5 25 = 2 6) Write the equation in its equivalent logarithmic form. 7) 62 = 7) 2

3 Evaluate the epression without using a calculator. 8) log 10 10,000 8) 9) log ) 10) log ) 11) 2 log ) 12) log ) Find the domain of the logarithmic function. 13) f() = log 5 ( + 7) 13) 14) f() = log 3 ( - 6)2 14) 15) f() = ln ) Evaluate or simplify the epression without using a calculator. 16) log ) 3

4 17) 8 log ) 18) ln e3 18) 19) ln 7 e 19) 20) ln 1 20) Evaluate the epression without using a calculator. 21) ln e12 21) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 22) log 6 (7 11) 22) 23) log 4 (16) 23) 24) log (10,000) 24) 25) log ) 4

5 26) log ) 27) log ) 28) log ) 29) logd 9 29) 30) log ) 31) log 6 3 y8 31) 32) log ) 33) ln 6 ey 33) 5

6 34) log y z2 34) Use properties of logarithms to condense the logarithmic epression. Write the epression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic epressions. 35) log c m + log c n 35) 36) 6 ln ln y 36) 37) log 6 ( - 6) - log 6 ( - 1) 37) 38) 3log 6 + 5log 6 ( - 6) 38) Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 39) log ) 40) log ) Solve the equation by epressing each side as a power of the same base and then equating eponents. 41) 4 = 64 41) 6

7 42) = ) Solve the eponential equation. Epress the solution set in terms of natural logarithms. 43) 2 5 = ) 44) e + 5 = 2 44) Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 45) 10 = ) 46) e = ) 47) 3 = 12 47) 48) 7 = ) Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic epressions. Give the eact answer. 49) log 2 = 5 49) 50) log 4 ( + 3) + log 4 ( - 3) = 2 50) 7

8 51) ln = 5 51) 52) ln = 7 52) 53) ln + 2 = 7 53) 54) ln 4 + ln ( - 1) = 0 54) Solve. 55) The value of a particular investment follows a pattern of eponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the eponential growth model A = 3200e0.06t. How much did you initially invest in the account? 55) 56) The value of a particular investment follows a pattern of eponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the eponential growth model A = 1600e0.052t. By what percentage is the account increasing each year? 56) Solve the problem. 57) The logistic growth function f(t) = 71, e-1.2t models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 7 weeks? 57) 8

9 440 58) The logistic growth function f(t) = describes the population of a species of e-0.27t butterflies t months after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain? 58) 59) The logistic growth function f(t) = 320 describes the population of a species of e-0.22t butterflies t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the habitat? 59) Determine whether the given ordered pair is a solution of the system. 60) (4, 5) + y = 9 - y = -1 60) 61) (5, -1) + y = -6 - y = -4 61) Solve the system of equations by the substitution method. 62) y = 2-4 3y + 9 = ) Solve the system by the addition method. 63) 4 + 7y = y = 18 63) 64) 4 + y = y = -1 64) 9

10 65) 5-6y = y = 40 65) Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to epress their solution sets. 66) y = ) -8-4y = 16 67) 2-4y = y = ) Determine if the given ordered triple is a solution of the system. 68) (4, 5, 3) + y + z = 12 - y + 4z = y + z = 20 68) 69) (-4, 4, 3) + y + z = 3 - y + 2z = y + z = 15 69) Solve the system of equations. 70) + y + z = 0 - y + 4z = y + z = -4 70) Evaluate the determinant. 71) ) 10

11 72) ) Use Cramer's rule to solve the system. 73) 2 + 3y = y =-23 73) 74) -2-2y= y = 23 74) Evaluate the determinant. 75) ) 76) ) Use Cramer's rule to determine if the system is inconsistent system or contains dependent equations. 77) 3 + y = 8 77) y = 32 78) 3 + 6y = y = 34 78) 11

12 Answer Key Testname: PATTERSON141REVIEW3-REAL 1) y ) C 3) 6 y ) 0.37 mg 5) $82, ) 52 = 25 7) log 6 = 2 8) 4 9) -2 10) 0 11) 18 12) 14 13) (-7, ) 14) (-, 6) or (6, ) 15) (8, ) 16) -2 17) ) ) ) 0 21) 12 22) log log ) 2 + log 4 12

13 Answer Key Testname: PATTERSON141REVIEW3-REAL 24) 4 + log 25) log log ) log ) 6log 3 28) -2log ) 9logd 30) log log log ) 3log 6-8log 6 y 32) log 4 ( + 3) - 4log 4 33) 1 6 ln y ) 1 7 log log 3 y - 2log 3 z 35) log c (mn) 36) ln 6 4 y 37) log ) log 6 3( - 6) 5 39) ) ) {3} 42) {27} ln ) 5 ln 2 44) {ln 2-5} 45) ) ) ) ) {32} 50) {5} 51) e5 52) e 2/3 53) {e14-2} 54) { 5 4 } 55) $ ) 5.2% 57) 46,346 people 58) 440 butterflies 59) 40 butterflies 60) solution 61) not a solution 62) {(-4, -12)} 13

14 Answer Key Testname: PATTERSON141REVIEW3-REAL 63) {(1, -2)} 1 64) 2,-1 65) {(4, 8)} 66) {(, y) 2 + y = -4} 67) 68) solution 69) not a solution 70) {(-4, -1, 5)} 71) 6 72) ) {(-5, 2)} 74) {(1, 7)} 75) ) ) system contains dependent equations 78) system is inconsistent 14

Solve algebraically. 1) 7 - a -4 1) Solve algebraically. Write answer in set builder or interval notation. 2) 4m m - 7 2)

Solve algebraically. 1) 7 - a -4 1) Solve algebraically. Write answer in set builder or interval notation. 2) 4m m - 7 2) Chapter 9 & 10 Practice. The following is an aid to study for the Chapter 9 & 10 eam. Disclaimer: The actual eam is different. You do need to show work on the actual eam and will not be given credit for