MATH COLLEGE ALGEBRA/BUSN - PRACTICE EXAM #2 - SUMMER DR. DAVID BRIDGE

Transcription

1 MATH 13 - COLLEGE ALGEBRA/BUSN - PRACTICE EXAM # - SUMMER DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the piecewise linear function. -, 1 1) f() = + 1, < 1 ) f() = -, > 0 1, 0

2 3) f() = -, 1 +, > Graph the function. ) f() =

3 ) f() = ) = Write a cost function for the problem. Assume that the relationship is linear. 7) An electrician charges a fee of $0 plus $ per hour. Let C() be the cost in dollars of using the electrician for hours. C() = - 0 C() = 0 - C() = + 0 C() = 0 + 8) Fied cost, $30; items cost $90 to produce C() = C() = C() = C() = ) Marginal cost, $0; 70 items cost $3800 to produce C() = C() = C() = C() =

4 Solve the problem. ) At a manufacturing plant, the total cost (in dollars) to produce items is C() =.8 +,000. What is the marginal cost per item? $,00.8 $.8 $,99. $,000 11) At a manufacturing plant, the total cost (in dollars) to produce items is C() = ,000. What is the average cost per item? $30,000 $.3 $30,000 + $.3 $30,00.3 1) Assume that the sales of a computer retail store are approimated b a linear function. Sales were $890,000 in 198 and $,0,000 in Let = 0 represent 198. Find the equation giving earl sales. Estimate sales in = 3, ,000 = 3,917,00 in 1993 = 88, ,000 = 3,8,999 in 1993 = 3, ,000 =,30,000 in 1993 = 3, ,000 = 3,8,000 in ) A house was purchased for $77,000. After 7 ears the value of the house was $8,000. Assume that the appreciation in value is given b a linear equation. Find the equation. = 77, = 77, = 8,000 = 00 1) A lumber ard has fied costs of $ a da and variable costs of $1.00 per board-foot produced. The compan gets $.0 per board-foot sold. How man board-feet must be produced dail to reach the equilibrium point? 3173 board-feet 710 board-feet 00 board-feet 70 board-feet Determine the verte of the parabola. 1) f() = (3, 0) (7, 3) (3, 7) (0, 7) 1) = -3( - 3) + (-, -3) (-3, ) (, 3) (3, ) Find the - and -intercepts. If no -intercepts eist, state so. 17) f() = (, 0), (0, 8) (8, 0), (0, ) (-8, 0), (0, ) (, 0), (0, -8) 18) f() = ±, 0, (0, 1) - ±, 0, (0, 1) - ±, 0, (0, -1) - ±, 0, (0, -1) 19) f() = No -intercepts, (0, -1) 3 ± 73, 0, (0, -1) 3 ± 73, 0, (0, 1) No -intercepts, (0, 1) Find the rule of a quadratic function whose graph has the given verte and passes through the given point. 0) verte (, ); point (, 3) f() = ( + ) + f() = ( - ) - f() = ( - ) + f() = ( + ) + 1) verte (, -); point (, -1) f() = -( - ) - f() = ( - ) - f() = ( - ) - f() = -( + ) -

5 Graph the parabola. ) = ) f() = ( - )

6 ) = -( + ) + 3 ) f() = Solve the problem. ) The manager of a CD store has found that if the price of a CD is p() = -, then CDs will be sold. An epression for 8 the total revenue from the sale of CDs is R() = - 8 Find the number of CDs that will produce maimum revenue. 8 30

7 7) John owns a hotdog stand. He has found that his profit is represented b the equation P = , with P being profits and the number of hotdogs. How man hotdogs must he sell to earn the most profit? hotdogs hotdogs 3 hotdogs 33 hotdogs 8) John owns a hotdog stand. His dail profit is represented b the equation P = , with P being profits and the number of hotdogs. What is the most profit he can earn in a da? $10 $ $99 $9 Graph the polnomial function. 9) f() = ) P() = 3( + 1)( - 1)

8 Solve the problem. 31) The graph of a function is given below. Tell whether the graph could possibl be the graph of a polnomial function. If it could be the graph of a polnomial function, tell which of the following are possible degrees for the polnomial function: 3,,,. es; 3, es; onl es; onl es;, 3) The graph of a function is given below. Tell whether the graph could possibl be the graph of a polnomial function. If it could be the graph of a polnomial function, tell which of the following are possible degrees for the polnomial function: 3,,,. es;, es; 3, es; onl no Graph the rational function. 1 33) f() = + 1

9 3) f() = Give the equation of the vertical asmptote(s) of the rational function. 3) g() = + = = 0 = - = - 3) g() = = = 8 = = Give the equation of the horizontal asmptote of the rational function. 37) g() = + = = = = 0 38) f() = = 7 = = 7 = 0

10 Graph the function. 39) f() = ) f() =

11 Provide an appropriate response. 1) The graph of an eponential function is given. Which of the following is the correct equation of the function? - - = 1.8 = 0. = 0.31 =. ) The graph of an eponential function is given. Which of the following is the correct equation of the function? - - = 0. =.8 = 0.73 = 3.9 Solve the problem. 3) An economist predicts that the buing power B() of a dollar ears from now will decrease according to the formula B() = How much will toda's dollar be worth in 3 ears? Round the answer to the nearest cent. $0.98 $0.80 $.78 $.79 ) Assume eponential growth; that is, use the formula P = P 0 a t. A bacterial culture has an initial population of 00. If its population grows to 7000 in hours, what will it be at the end of hours? 07,03 0,19 ) Assume eponential deca; that is, use the formula P = P 0 a t. A bacterial culture has an initial population of,000. If its population declines to 3000 in hours, what will it be at the end of 8 hours? ) The sales of a mature product (one which has passed its peak) will decline b the function S(t)= S 0 e-at, where t is time in ears. Find the sales after ears if a = 0. and S 0 = 9, ,18, , Write in logarithmic form. 7) 7 = 9 7 = log 9 = log = log 7 = log 7 9 8) -3 = = log -3 = log = log = log 1/8 9) e - = = log - e = ln - - = ln e = log

12 Find the value of the epression. 0) log 8 1 1) log Write the epression as the logarithm of a single number or epression with a coefficient of 1. Assume all variables represent positive numbers. ) log + log - log log 3 log 1 log 11 log 3 3) log w + log z - log ( - ) log ( - ) w z log w ( - ) z log w z ( - ) log w z ( - ) Write the epression as a sum and/or a difference of logarithms with all variables to the first degree. ) log 8r 3 s log 11 + log r + log s log r + log s log log r + log s log r + log s ) log 9 log - log 9 log + log + log 9 + log log + log - log 9 - log log - 9 log Evaluate the epression. ) log ) log

13 Graph the function. 8) = log Solve the eponential equation. 9) 3 (1-3) = ) 7 = ) 7 = Find the simple interest. Round to the nearest cent. ) $00 at 1% for 1 ears Interest = $ Interest = $.80 Interest = $33.33 Interest = $8.00 3) $30 at 1% for months Interest = $ Interest = $3.00 Interest = $3.00 Interest = $.3 Find the present value of the future amount. ) $1,000 for months; mone earns 9% $1,883.7 $1,988.9 $111.8 $1,78.90 Solve the problem. ) Allan borrowed $800 from his father to bu a car. He repaid him after months with interest of %. Find the total amount he repaid. $97.00 $ $03.00 $ ) Tuition of $00 is due when the spring term begins, in 9 months. What amount should a student deposit toda, at %, to have enough to pa tuition? $88.0 $111.9 $.83 $00.00

14 Find the compound amount for the deposit. Round to the nearest cent. 7) $19,000 at 1% compounded annuall for 1 ears $9,8.13 $8,0.00 $0,90.00 $8, ) $1900 at % compounded quarterl for ears $0.00 $ $097. $80. Find the compound interest earned b the deposit. Round to the nearest cent. 9) $3000 at 1% compounded semiannuall for ears $ $317. $37. $1.1 70) $830 at 7% compounded annuall for 0 ears $171.7 $13.90 $381.8 $11.00 Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 71) 11% compounded semiannuall 11.% 11.30% 11.00% 11.7% 7) 3% compounded monthl 3.0% 3.0% 0.3%.03% Find the amount that should be invested now to accumulate the following amount, if the mone is compounded as indicated. 73) $00 at 7% compounded annuall for 1 r $ $ $11.03 $30.8 7) $3000 at 8% compounded semiannuall for 8 r $101.7 $10.81 $18.9 $ Solve the problem. 7) A bank gives ou two options to choose from for our investments: Option A: 8% annual interest rate compounded earl; and Option B: 7.9% annual interest rate compounded quarterl. Decide which is the better investment at the end of ears. Option B Option A 7) Mark and Kate are establishing a fund for their son's college education. What lump sum must the deposit in an account that gives 8% annual interest rate, compounded monthl, in order for them to have $0,000 in the fund at the end of ears? $7,031.1 $8,331.1 $31,07.1 $9, ) $19 is deposited into a savings account at % interest, compounded monthl. To the nearest ear, how long will it take for the account balance to reach $9? 18 ears 1 ears 0 ears 8 ears Find the value. s 78) s 79) Find the future value of the ordinar annuit. Interest is compounded annuall, unless otherwise indicated. 80) R = $0, i = 0.0, n = $3.0 $3.71 $97.3 $3.0 81) R = $00, i = 9% interest compounded quarterl for 1 ears $30,73.18 $30,9.33 $1, $1,0.

15 Find the periodic pament that will render the sum. 8) S = $39,000, interest is 8% compounded annuall, paments made at the end of each ear for 1 ears $ $3.98 $3.8 $ ) S = $3,000, interest is 18% compounded monthl, paments made at the end of each month for 3 ears $1.70 $38. $8.1 $09.80 Solve the problem. 8) If Bob deposits $000 at the end of each ear for ears in an account paing % interest compounded annuall, find the amount he will have on deposit. $3,0.00 $30,.0 $18,0.00 $1,0.00 8) Laura wants to start an IRA that will have $870,000 in it when she retires in 9 ears. How much should she invest monthl in her IRA to do this if the interest is 1% compounded monthl? $07. $3,83.0 $1.1 $133.1

16 Answer Ke Testname: MATH 13 - PRACTIVE EXAM # 1) C ) D 3) B ) B ) D ) A 7) C 8) B 9) B ) B 11) C 1) D 13) B 1) D 1) C 1) D 17) C 18) B 19) D 0) C 1) A ) A 3) D ) C ) C ) B 7) C 8) B 9) A 30) D 31) D 3) C 33) D 3) A 3) C 3) C 37) D 38) A 39) C 0) D 1) D ) A 3) B ) D ) D ) A 7) D 8) C 9) C 0) D 1) C ) B 3) D ) C ) C ) C 7) C 8) C 9) B 0) B 1) D ) D 3) B ) A ) D ) A 7) A 8) D 9) D 70) C 71) B 7) B 73) C 7) A 7) A 7) A 77) C 78) B 79) C 80) C 81) B 8) D 83) C 8) A 8) C