21Test1B - ' 5 Somme/0 MATH 122, SECTION 021 TEST 113 You...

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Unformatted text preview: ' 5 Somme/0 MATH 122, SECTION 021 TEST 113 You may use a calculator, but not the TI—89. Show all work for full credit. 1. Write the equation of the exponential function that passes through the points (37 270) and (5,972). (8 points) 270: Be “3° 73.2. , lief 270: 3/5"“) 777= 172%) Z70 £6le . a : 62K )2: 2K -051”: £00.30 = 1/18 77: )2506 Maw ‘AE— all Z t K; ,fllsn P: 2. Complete the table of values. (6 points) a. f is a linear function. u 18 \/7 ‘HO b. 9(30) is an exponential function. .- mgr-mm:- L/i il XLZ 3. Rewrite the function P = 200060‘48t in the form P = Pout. (8 points) 0H8 a:€’< ...—-.> age P )t [+r= llaleDfl’ =20c>c> mole _ a= mum f-O- (0’00? Fill in the blank: Annual Rate: 2’ Continuous Rate: M 4. Determine whether each of the following is a power function. For all power functions7 give the values of k: and p. (6 points) a. y = 2(75”) 0. y = 56/5 Net a Power ‘1 5 5X [/4 FuflC‘lTo’l 14= 5 2 5. Sam goes to Europe for Spring Break with $4500. Find a formula for the balance B of his money after t days in Europe if he spends a. 13% of his money each day. (4 points) B= L/Soo(a87)t b. $360 each day. (4 points) B = 9500 — 3W 6. If an investment increases exponentially from $5000 in 2008 to $8400 in 2011, What is the annual (not continuous) growth rate? (8 points) m=guzmw3 _ l+r=H8878 5030 5m “08: as F=0JS$78 a= $1887? 7. Suppose your student organization decides to sell T—shirts to raise money. It costs a total of $155 to produce 20 T-shirts and a total of $320 to produce 50 T—shirts. You decide you should sell the T—shirts for $8 per shirt. a. Find a linear equation expressing the cost, C (q), of producing q shirts. (5 points) m: =55 50-20 6 *155= 553-20) 6-155 = 5. — no b. Find the revenue function, R(q). (2 points) 0. How many T-shirts do you need to sell to make profit? How did you determine this? 3 oint ( p S) We mush 56“ $\’ 82 6.52 +95 252 = 45 +8 mal‘C pr 3‘" 2H8 8. Suppose a company’s demand function is given by q = —40p + 2200, Where p is the price at which q items will be sold. Determine the vertical intercept and explain What this means for the company. (6 points) ?, -ydoyzzoo Verbena ink/«pi? 2:2200 I? m rims are 55an W Page) Hammers W“ alert/lama! 2200 lire/W5. 9. The size of a bacteria colony triples every 8 hours. If the bacteria is growing exponen— tially, how long will it take the number of bacteria to be 5 times the original amount? I (8 points) é 3:100 Le as) _ 0.13725 300:1086 . 5.095% "’ 73?; ‘ mo "e‘; 3¢ 6 K 5: 6 0.13715 M3: l/hZ g ['46: M6 13 = 8" ’4—5 ‘ Dig—“ft % a“ K K= 0J3? [a a=l./47> 10. The promoters of a local festival estimate that 25 hours after the doors open at 9AM, y‘ the attendance A of people at the festival can be estimated by A(t) = ~28t2 + 3922: + 25 people. Calculate the average rate of change in the attendance between 1PM and 6PM. Give units. (8 points) w a M tag—49 5 /¥§§41fl5= 25/50/16. 6PM —> £4 4 11. The distance an object falls is directly proportional to the square of the time that it has been falling. If an object falls 144 feet in 3 seconds, how far will it fall in 7 seconds? Give units. (6 points) D: Ktz z ‘D ; )[piz W“ K (5) 13551067); K: Mo b: 12. I am saving money for.retirement and my investment is growing exponentially. In the year 2003, I had $5,000. and by 2011, I had $12,000. If I can“ retire once I have $250,000, in What year will I be able to retire? (10 points) ti 200319615=O . « \. m) ’ 0"ng 120w=5a3sea - Z@?$QO€ 15;): San: _. 5000 5559 XL 50 v 0.10975 M2.” = W p . Lnéo= .lnc ’ [(12.4 =fi/é . 2 ,2 /,,_5_c_3 = 0.49325 '2’?" a — valor (or a=/,Iw> £45.74? [can web/8 M 13. Determine the intervals over which f is increasing, decreasing, concave up, and concave down. Give your answers in interval notatién. (8 points) Increasing: ’60 ’2 U (4 a) Decreasing: _LZJ£___—_ Concave up: AW— Concave down: “as ‘ ...
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21Test1B - ' 5 Somme/0 MATH 122, SECTION 021 TEST 113 You...

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