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Slope & y-intercept – Class WorkIdentify the slope and y-intercept for each equationm=0b=7m=-2b=0m=3b=-4y=3x-42. y=-2x3. y=7m=4b=27m=0b=0m=undefb=nonex=-55. y=06. y-3=4(x+6)2496185789940m=47 b=-2m=-23 b=3m=-12 b=-5y+2=-12(x+6)8. 2x+3y=99. 4x-7y=14Write the equation of the given line in slope-intercept form and match with the correct alternate form.y=-57x+5 IIIy+4=-12x-2No Alternate Form(Slope Undefined)5x+7y=35y-6=3(x-4)2x-7y=14y-6=0(x+2)Ay=0x+6 VIBy=-12x-3 ICy=27x-2 VD y=3x-6 IVEx=8 IIFWrite an equation: Cal C. drives past mile marker 27 at 11am and mile marker 145 at 1pm.y=59x+27Slope & y-intercept – HomeworkIdentify the slope and y-intercept for each equationm=-5b=-2m=0b=-2m=3b=0y=-5x-218. y=3x19. y=-2m=2b=-12m=undefb=nonem=undefb=nonex=1021. x=022. y-4=2(x-8)m=13 b=-2m=-34 b=3m=-25 b=-72495550861695y+3=-25(x+10)24. 3x+4y=1225. 2x-6y=12Write the equation of the given line.y=32x-4 Vy+4=-4x-3x+3y=-1y+6=0(x-1)No Alternate Form(Slope Undefined)3x-2y=82x-9y=2Ay=-4x+8 IBx=-6 IVC y=-13x-1 IIDy=29x-2 VIEy=0x-6 IIIFWrite an equation: Cal C. drives past mile marker 45 at 11am and mile marker 225 at 2pm.y=60x+45Standard Form – Class WorkFind the x and y intercepts for each equation.x:52,0 y:(0,2)x:6,0y:(0,4)2x+3y=1234. 4x+5y=10x:94,0 y:nonex:10,0y:(0,-103) x-3y=1036. 4x=9y=0x:infinitey:(0,0)Standard Form – HomeworkFind the x and y intercepts for each equation.x:2,0y:(0,7)x:5,0y:(0,-3)3x-5y=1539. 7x+2y=14x:noney:(0,7)x:9,0y:(0,-9)x-y=941. y=7x:0,0y:infinitex=0Horizontal and Vertical Lines – Class WorkWrite the equation for the described liney=3x=1vertical through (1,3)44. horizontal through (1,3)vertical through (-2, 4)46. horizontal through (-2, 4)y=4x=-2Horizontal and Vertical Lines – HomeworkWrite the equation for the described liney=-10x=4vertical through (4,7)48. horizontal through (8,-10)vertical through (8, -10)50. horizontal through (4, 7)y=7x=8Parallel and Perpendicular Lines – Class WorkWrite the equation for the described line in slope intercept formy=3x-8y=-13x+2 Parallel to y=3x+4 through (3,1)52. Perpendicular to y=3x+4 through (3,1)y=2x-10 y=-12x Parallel to y=-12x+6 through (4,-2)54. Perpendicular to y=-12x+6 through (4,-2)Parallel to y=5 through (-1,-8)56. Perpendicular to y=5 through (-1,-8)x=-1 y=-8 Parallel and Perpendicular Lines – HomeworkWrite the equation for the described line in slope intercept formy=12x+4 y=-2x-11 Parallel to y=-2x+1 through (-6,1)58. Perpendicular to y=-2x+1 through (-6,1)y=-3x-18 y=13x+2 Parallel to y=13x-5 through (-6,0)60. Perpendicular to y=13x-5 through (-6,0)y=7 x=-3 Parallel to x=5 through (-3,7)62. Perpendicular to x=5 through (-3,7)Point-Slope Form – Class WorkWrite the equation for the described line in point slope form.y-3=-2(x+4)y-1=6(x-5)Slope of 6 through (5,1)64. Slope of -2 through (-4,3)Slope of 1 through (8,0)66. Perpendicular to y=-2x+1 through (1,-6)y+6=12(x-1) y-0=1(x-8)Convert the following equations to slope-intercept form and standard formy-4=5(x+3)68. y=-2(x-1)69. y+7=15(x-10)y=15x-9 x-5y=45y=-2x+22x+y=2y=5x+195x-y=-19Point-Slope Form – HomeworkWrite the equation for the described line in point slope form.y+9=3(x-0)y+2=-4(x-4)Slope of -4 through (4,-2)71. Slope of 3 through (0,-9)Slope of 1/4 through (6,0)73. Perpendicular to y=-12x+6 through (5,-2)y+2=2(x-5)y-0=14(x-6) Convert the following equations to slope-intercept form and standard formy=16x-6 x-6y=36y=-4x+274x+y=27y=7x-117x-y=11y-3=7(x-2)75. y+1=-4(x-7)76. y+3=16(x-18)Writing Linear Equations – Class WorkWrite an equation based on the given information in slope intercept form.y=2x-14 y=-12x+52 A line through (7,-1) and (-3,4)78. A line through (8,2) and (6,-2)y=-2x-10 A line perpendicular to y-7=12(x+2) through (-1,-8)y=23x+1 A line parallel to 4x-6y=10 through (9,7)y=x+1 A function with constant increase passing through (2,3) and (8,9)y=1.00x+1.70 The cost of a 3.8 mile taxi ride cost $5.50 and the cost of a 4 mile ride costs $5.70A valet parking services charges $45 for 2 hours and $55 for 3 hoursy=10x+25 Writing Linear Equations – HomeworkWrite an equation based on the given information in slope intercept form.y=0x+2 y=2x+1 A line through (4,9) and (-5,-9)85. A line through (-8,2) and (8,2)y=-32x+5 A line perpendicular to 4x-6y=10 through (2,2)y=12x+1 A line parallel to y-7=12(x+2) through (2,2)y=-2x+7 A function with constant decrease passing through (2,3) and (8,-9)y=2.50x-1.25 The cost of a 3.8 mile taxi ride cost $8.25 and the cost of a 4 mile ride costs $8.75A valet parking services charges $55 for 2 hours and $75 for 4 hoursy=10x+35 Absolute Value Functions – Class WorkGraph each function. For each, state the domain and range.3838576512446D: RR:[0,∞) 457200512445D: RR:[0,∞) y=x-492. y=2x3895725513715847725513715D: RR:[0,∞) D: RR:[0,∞) y=2x-494. y=2x3838575486410533400581660D: RR:[3,∞) D: RR:[3,∞) y=x+396. y=2x+33514725601345457200553720D: RR:(-∞,-3] D: RR:(-∞,0] y=-x-398. y=-12x-3Absolute Value Functions – HomeworkGraph each function. For each, state the domain and range.4010025521970514350521970D: RR:[0,∞) D: RR:[0,∞) y=x+2100. y=3x35623506661141009650551815D: RR:[0,∞) D: RR:[0,∞) y=3x+2102. y=23x3562349723900514350571500D: RR:[-1,∞) D: RR:[-1,∞) y=x-1104. y=23x-13562350667384514349553085D: RR:(-∞,4] D: RR:(-∞,0] y=-x+4106. y=-14x+4Greatest Integer Functions – Class WorkGraph each function. For each, state the domain and range.3990975550545D: RR:Z 732790516494D: RR:Z y=[x-4]108. y=[2x]3990975485140790575485140D: RR:2Z D: RR:Z y=[2x-4]110. y=2[x]3952875467360762000467360D: RR:2Z+1 D: RR:Z y=x+3112. y=2x+33562350601345733425525146D: RR:12Z D: RR:Z y=-[x-3]114. y=-12x-3Greatest Integer Functions – HomeworkGraph each function. For each, state the domain and range.4133850459105638175459105D: RR:Z D: RR:Z y=[x+2]116. y=[3x]3533775612775847725508000D: RR:23Z D: RR:Z y=[3x+2]118. y=23[x]3533775594360495300527685D: RR:23Z D: RR:Z y=x-1120. y=23x-13543300671195638175509270D: RR:14Z D: RR:Z y=-[x+4]122. y=-14x+4Identifying Exponential Growth and Decay – Class Work3248025512445238125512445State whether the given function exponential growth or decay. Identify the horizontal asymptote and the y-intercept.A BDecayHA: y=0y-int: (0,1)GrowthHA: y=0y-int: (0,1)GrowthHA: y=0y-int: (0,12) GrowthHA: y=0y-int: (0,3)y=3(4)x125. y=12(3)xDecayHA: y=-7y-int: (0,-5)DecayHA: y=4y-int: (0,5)y=12x+4127. y=214x-7DecayHA: y=0y-int: (0,17)DecayHA: y=50y-int: (0,150)y=10013x+50129. y=17(4)-xy=1234-x+6131. y=12(5)-x-2DecayHA: y=2y-int: (0,-112) GrowthHA: y=6y-int: (0,18)Identifying Exponential Growth and Decay – Homework3105150575310485775527685 State whether the given function exponential growth or decay. Identify the horizontal asymptote and the y-intercept.A BGrowthHA: y=2y-int: (0,3)DecayHA: y=2y-int: (0,3)DecayHA: y=0y-int: (0,5)DecayHA: y=0y-int: (0,3)y=325x134. y=5(3)-xGrowthHA: y=-7y-int: (0,-3)DecayHA: y=4y-int: (0,10)y=612x+4136. y=4(25)x-7GrowthHA: y=0y-int: (0,17)GrowthHA: y=50y-int: (0,150)y=10013-x+50138. y=17(4)xy=1234x+6140. y=25(7)x-1GrowthHA: y=-1y-int: (0,-35) DecayHA: y=6y-int: (0,18)Graphing Exponentials – Class WorkGraph each equation.3438525388620581025340995y=3(4)x142. y=12(3)x3543300371475733425371475y=12x+4144. y=214x-73543300358775914400358775y=10013x+50146. y=17(4)-xy=1234-x+658102588900Graphing Exponentials – HomeworkGraph each equation3895725407670752475407035y=325x149. y=5(3)-x3543300366394618490365760y=612x+4151. y=4(25)x-73895725382270933450382270y=10013-x+50153. y=17(4)xy=1234x+675247555245Intro to Logs – Class WorkWrite each of the following in log form.log327=3log216=4log100=2102=100156. 24=16157. 27=33Write each of the following in exponential form.73=34362=3653=125log5125=3159. log636=2160. log7343=3Solve the following equationsx=6x=3log464=x162. log264=xy=216y=243log3y=5164. log6y=3b=10b=3logb81=4166. logb10=1log5(x-2)=log5(2x-8)168. log4(2x+7)=log4(4x-9)x=8x=6Intro to Logs – HomeworkWrite each of the following in log form.log381=4log232=5log981=292=81170. 25=32171. 81=34Write each of the following in exponential form.34=8144=25682=64log864=2173. log4256=4174. log381=4Solve the following equationsx=7x=5log41024=x176. log2128=xy=2401y=625log5y=4178. log7y=4b=2b=10logb1000=3180. logb1024=10log5(x+2)=log5(3x-8)182. log4(3x-6)=log4(x+10)x=8x=5Properties of Logs – Class WorkUsing Properties of Logs, fully expand each expression1+2log7m-2(log7u+log7v)log6w-2log6x-log6ylog4x+3log4y+4log4zlog4xy3z4184. log6wx2y185. log77m2uv2Using log25≈2.3219 and log210≈3.3219, evaluate the following4.32196.64385.6438log250187. log2100188. log220Using Properties of Logs, rewrite the expression as a single log.logx+logy-logz190. 1-3log5m191. 5logk-3(logr+logt)logk5rt3 logxyz log55m3 Solve the following equationsx=1x=60.75log3x+ log34 =5193. log2x+ log2(x+3)=2x=7x=1log3x+12log34 =14log316195. log3x+log3(x-2)=log335x=8x=82log3x- log34 =log316 197. log3(x+3)+ log3(x-2) =log366 Properties of Logs – Home WorkUsing Properties of Logs, fully expand each expression1+4log8m-3(2log8u+log8v)1+log4w-2log4x1+log3x+2log3y+5log3zlog33xy2z5199. log44wx2200. log88m4u2v3Using log23≈1.5850 and log218≈4.1699, evaluate the following6.345.1699-2.5849log216202. log236203. log281Using Properties of Logs, rewrite the expression as a single log.logf5g2h6 log44m2 logx2y3z4 2logx+3logy-4logz205. 1-2log4m206. 5logf-2logg-6loghSolve the following equationsx=4x=3.375log34x+ log32 =3208. log2x+ log2x-3=2x=3x=64log3x- log34 =log316 210. log3x2+ log3x =log327 2log3x- log39 =log325 212. log3(2x+3)+ log3(x-2) =log372 x=6.5x=15Common Logs – Class WorkSolve for the variable.b=log8log4+2≈3.5 x=2 x=log18log7≈1.485 7x=18214. 3x+4=27x215. 4b-2=8t=2log5+2log4log5-log4≈26.85 n=2log7log7-log3≈4.593 d=log29log5+32≈2.546 52d-3=29217. 7n-2=3n218. 4t+2=5t-2Find the approximate value for eachlog36220. log517221. log6372.01531.76041.6309Common Logs – Home WorkSolve for the variable.b=log42log9+6≈7.701 x=8 x=log21log8≈1.464 8x=21223. 64x-1=42x+5224. 9b-6=42t=log32+log18log32-log18≈11.047 n=5log2log7+log2≈1.313 d=log40log19+13≈0.751 193d-1=40226. 25-n=7n227. 18t+1=32t-1Find the approximate value for eachlog310229. log520230. log6301.89821.86142.0959e and ln – Class WorkSolve the following equationsx=1x=10x=6elnx=6232. elnx-4=6233. lnex+5=6xx=ln13-1≈-2.099 x=ln72≈0.973 x=23lne2x-8=4235. e2x=7236. 3e(x-1)+9=10x=e6≈403.429x=e7-1≈1095.633lnx+1=7238. ln(x)+1=7e and ln – HomeworkSolve the following equationsx=11x=2x=3eln2x=6240. 5elnx-4=6241. lne2x-5=6+xx=ln12-12≈-0.847 x=ln6-13≈0.264 x=14lne3x+9=21243. e3x+1=6244. 4e(2x+1)+8=10x=e9+1≈8104.084x=e10≈22026.466lnx-1=9246. ln(x)-1=9Growth and Decay – Class WorkSolve the following problems$290.19$250 is deposited in an account earning 5% that compounds quarterly, what is the balance in the account after 3 years?6.75 gramsA bacteria colony is growing at a continuous rate of 3% per day. If there were 5 grams to start, what is the mass of the colony in 10 days?17.33 daysA bacteria colony is growing at a continuous rate of 4% per day. How long till the colony doubles in size?$15,831.96If a car depreciates at an annual rate of 12% and you paid $30,000 for it, how much is it worth in 5 years?r=0.012=1.2%77.07 daysAn unknown isotope is measured to have 250 grams on day 1 and 175 grams on day 30. At what rate is the isotope decaying? At what point will there be 100 grams left?$3,629.55An antique watch made in 1752 was worth $180 in 1950; in 2000 it was worth $2200. If the watch’s value is appreciating continuously, what would its value be in 2010?A furniture store sells a $3000 living room and doesn’t require payment for 2 years. If interest is charged at a 5% daily rate and no money is paid early, how much money is repaid at the end?$3,315.49Growth and Decay – HomeworkSolve the following problems$13,12211.55 days19.028 grams$58.66$10,456.51$4,802.66$50 is deposited in an account that earns 4% compounds monthly, what is the balance in the account after 4 years?A bacteria colony is growing at a continuous rate of 5% per day. If there were 7 grams to start, what is the mass of the colony in 20 days?A bacteria colony is growing at a continuous rate of 6% per day. How long till the colony doubles in size?If a car depreciates at an annual rate of 10% and you paid $20,000 for it, how much is it worth in 4 years?r=0.0096=0.96%144.57 daysAn unknown isotope is measured to have 200 grams on day 1 and 150 grams on day 30. At what rate is the isotope decaying? At what point will there be 50 grams left?An antique watch made in 1752 was worth $280 in 1940; in 2000 it was worth $3200. If the watch’s value is appreciating continuously, what would its value be in 2010?A $9000 credit card bill isn’t paid one month, the credit company charges .5% continuously on unpaid amounts. How much is owed 30 days later? (assume no other charges are made)Logistic Growth – Class WorkScientists measure a wolf population growing at a rate of 3% annually. They calculate the carrying capacity of the region to be 100 members.Pt+1=Pt+0.03Pt(1-Pt100)Write a logistic equation to model this situation.1200150250190Create a table that shows the pack population over the next 10 years if P1=302047875292736Draw a graph of the equationLogistic Growth – HomeworkA calculus class determines that a rumor spreads around the school at a rate of 15% per hour. The school population is 1600.Pt+1=Pt+0.15Pt(1-Pt1600)Write a logistic equation to model this situation.1209675479425Create a table that shows the number of people who know the rumor over the next 10 hours if the class that starts it has 20 members2129733168237Draw a graph of the equation4400550-76200Trig Functions – Class WorkUse the appropriate triangle to answer questions 267-274.1819.5≈0.923 7.519.5≈0.385 sinθ=268. cosθ=10.517.5≈0.6 187.5≈2.4 4876800626110tanθ=270. sinα=10.514≈0.75 1417.5≈0.8 cosα= 272. tanα=36.87° 67.38° θ= 274. α=5.36 A right triangle has a hypotenuse of 7 and an angle of 40°, find the larger leg.30.964° A right triangle has legs of 6 and 10 find the smaller acute angle.10.44 A right triangle has an angle of 50° and a longer leg of 8, find the hypotenuse.Trig Functions – HomeworkUse the appropriate triangle to answer questions 278-285.1517≈0.882 817≈0.471 4619625413385sinθ=279. cosθ=1620≈0.8 815≈0.533 4619625187960tanθ=281. sinα=1612≈1.333 1220≈0.6 cosα=283. tanα=53.13° 28.07° θ=285. α=7.794 5.321 30.256° A right triangle has a hypotenuse of 9 and an angle of 60°, find the larger leg.A right triangle has legs of 7 and 12 find the smaller acute angle.A right triangle has an angle of 20° and a longer leg of 5, find the hypotenuse.Converting Degrees and Radians – Class workConvert the following degree measures to radians and radian measures to degrees.5π4 7π36 120° 2π3290. 35°291. 225°280° 5π6 36° π5293. 150°294. 14π93π2 257.14° 31π18 310°296. 10π7297. 270°Converting Degrees and Radians – Class workConvert the following degree measures to radians and radian measures to degrees.10π9 5π12 300° 5π3299. 75°300. 200°35π36 340° 144° 4π5302. 175°303. 17π9350°305. 9π7306. 11π1835π18 110° 231.43° Graphing Sin, Cos, and Tan – Class WorkA sine max/min occurs at the exact same x-value as cosine zeros.What is the relationship between when a sine max/min value occurs and when a cosine zero occurs? The sine zeros are where tangent also has zeros. The cosine zeros are where tangent has vertical asymptotes.How do the zeros of the cosine and sine graphs relate to a tangent graph?Consider the domain of –π,π for sinθ, cosθ, and tanθtanxWhich function(s) is increasing on the entire interval?sinx, cosxWhich function(s) has a relative max?cosx,tanxWhich function(s) has a concave down interval followed by a concave up interval?Which function(s) has an undefined value of x on the interval?tanxGraphing Sin, Cos, and Tan – HomeworkA cosine max/min occurs at the exact same x-value as sine zeros.What is the relationship between when a cosine max/min value occurs and when a sine zero occurs? Tangent is concave down, then changes to concave up between the vertical asymptotes.How does the tangent function’s concavity change between asymptotes?Consider the domain of –π,π for sinθ, cosθ, and tanθnoneWhich function(s) is decreasing on the entire interval?sinx,cosx,tanxWhich function(s) has a zero?sinx,tanxWhich function(s) has a concave up interval followed by a concave down interval?Which function(s) has a relative minimum?sinx, cosxPositive and Negative Integer Power Functions – Class WorkFor each equation find limx→-∞, limx→0-f(x), limx→0+f(x), and limx→∞f(x).limx→-∞fx=∞limx→0-fx=0limx→0+fx=0limx→∞f(x)=∞limx→-∞fx=-∞limx→0-fx=0limx→0+fx=0limx→∞f(x)=∞fx=4x3318. fx=5x6limx→-∞fx=-∞limx→0-fx=0limx→0+fx=0limx→∞f(x)=-∞limx→-∞fx=∞limx→0-fx=0limx→0+fx=0limx→∞f(x)=-∞fx=-13x5320. fx=-x2limx→-∞fx=0limx→0-fx=∞limx→0+fx=∞limx→∞f(x)=0limx→-∞fx=0limx→0-fx=-∞limx→0+fx=∞limx→∞f(x)=0fx=4x-3322. fx=5x-6limx→-∞fx=0limx→0-fx=-∞limx→0+fx=-∞limx→∞f(x)=0limx→-∞fx=0limx→0-fx=∞limx→0+fx=-∞limx→∞f(x)=0fx=-13x-5324. fx=-x-2Positive and Negative Integer Power Functions – HomeworkFor each equation find limx→-∞f(x), limx→0-f(x), limx→0+f(x), and limx→∞f(x).limx→-∞fx=-∞limx→0-fx=0limx→0+fx=0limx→∞f(x)=-∞limx→-∞fx=-∞limx→0-fx=0limx→0+fx=0limx→∞f(x)=∞fx=3x9326. fx=-2x8limx→-∞fx=∞limx→0-fx=0limx→0+fx=0limx→∞f(x)=∞limx→-∞fx=∞limx→0-fx=0limx→0+fx=0limx→∞f(x)=-∞fx=-14x11328. fx=6x20limx→-∞fx=0limx→0-fx=-∞limx→0+fx=-∞limx→∞f(x)=0limx→-∞fx=0limx→0-fx=-∞limx→0+fx=∞limx→∞f(x)=0fx=3x-9330. fx=-2x-8fx=-14x-11332. fx=6x-20limx→-∞fx=0limx→0-fx=∞limx→0+fx=∞limx→∞f(x)=0limx→-∞fx=0limx→0-fx=∞limx→0+fx=-∞limx→∞f(x)=0Rational Power Functions – Class WorkChoose which function(s) fits the description provided.(A) fx=x13 (B) fx= 4x (C) f(x)=x16 (D) fx= 7xA and DB and Cundefined for negative real values334. limx→-∞fx=-∞A, B, C, and DDclosest to (10,1)336. limx→0+fx=0AB and Climx→0-fx=undefined338. closest to (10 , 3)Rational Power Functions – HomeworkChoose which function(s) fits the description provided.(A) fx=-x13 (B) fx= -4x (C) fx=-x16 (D) fx= -7xNoneA and DDomain is (-∞,∞)340. limx→∞fx=∞B and CBclosest to (5,-1.5)342. limx→0fx=undefinedRange is (-∞,0]344. closest to (10 ,- 1.5)CB and CRational Functions – Class WorkFor each of the following functions, name any discontinuities and tell whether they are non-removable or removable. Graph each function.3905250868680x=5 removablex=-5 non-removable628650868680x=2 removablex=-2 non-removableh(x)=3x2-4x-4x2-4346. gx= x-5x2-253705225734695504825734695x=3 non-removablex=6 removablejx= x2-12x+36x-6348. mx= x2-9x2-6x+9limx→3-f(x)= limx→3+f(x)=2;f3 is undefinedx=3 removableGraphs will vary.Any graph that would go through the point (3,2), but instead has a hole at that point.Rational Functions – HomeworkFor each of the following functions, name any discontinuities and tell whether they are non-removable or removable. Graph each function.3878004878205800100859155x=4 removablex=-4 non-removablex=2 removablex=-2 non-removableh(x)=x2-4x+4x2-4351. gx= x-4x2-163543300677545762000677864x=-7 non-removablex=6 removablejx= 2x2-8x-24x-6353. mx= x2-49x2+14x+49x=-5 removableGraphs will vary.Any graph that would go through the point (-5,1), but instead has a hole at that point.limx→-5-f(x)= limx→-5+f(x)=1;f-5 is undefinedUnit Review - Multiple ChoiceWhich equation has an x-intercept of (5,0) and a y-intercept of (0,-52)y+52=5(x-0)Cy-52=5(x-0)y=12(x-5)y=12(x+5)The equation of a line perpendicular to 2x+3y=7 and containing (5,6) is3x-2y=3Ay-6=-23(x-5)3x-2y=4y=23(x-6)A line with no slope and containing (3,8) has equationy=3By=8x=3x=8The vertex of y=-2x-1+7 is(2,7)D(-2,7)(-1,7)(1,7)4-32.7+0.5=-40C-36-32-28The equation that models exponential decay passing through (0,5) and a limx→∞fx=4 isDfx=5ex+4fx=-1ex+4fx=5e-x+4fx=-1e-x+4A forest fire spreads continuously, burning 10% more acres every hour. How long will it take for 1000 acres to be on fire after 200 acres are burning?B23.026 hours16.094 hours6.932 hoursnot enough informationBlog65=.116.8981.1131.308Given 4x=10, find xD2.5.602.4001.661logm=.345 and logn=1.223, find log10m2n3 A-1.979.6516.5078.473Which of the following would not influence the carrying capacity of a logistic growth modelthe population of a townCthe food supply in an ecological preservethe rate of spread of the fluthe area inside a Petri dishThe larger leg of a right triangle is 6 and the smallest angle is 20°, what is the hypotenuse?A6.3855.63817.54314.703How many degrees is 4π9?160°C110°80°62°An example of a function that is concave down and then concave up isfx=sinx on (0,π)Cfx=tanx on (0,π)fx=cosx on (0,π)fx=sinx on (-π,π)The function that has limx→0-fx=∞ and limx→0+fx=-∞ isfx= -3x3Cfx= -4x4fx= -3x-3fx= -4x-4The function hx=4x2-3x-14x2-1 has the following discontinuitiesAnon-removable discontinuity at x=±12removable discontinuity at x=±12non-removable discontinuity at x=12; removable discontinuity at x=-12non-removable discontinuity at x=-12; removable discontinuity at x=12Extended ResponseConsider the function hx=f(x)g(x), if fx= x2-2x-8 and gx=x2+8x+15limx→-∞hx=+1limx→∞hx=+1Use limit notation to describe the end behavior of h(x)x=-5, -3both non-removableName any discontinuities and whether they are removable or non-removable.m(x) is any polynomial with x+3 as a factor, or any rational function with x+3 as a factor of the numeratorjx=h(x)?m(x) and has a removable discontinuity at x=-3,what is m(x)?Entomologists introduce 20 of one variety of insect to a region and determine that the population doubles every 6 hours.A=20e0.1155tWrite an equation to model this situation.63.48 hoursWhat will the population be in 10 hours?Pt+1=Pt+0.1155Pt(1-Pt100000)If those same scientists determine that the region can support a maximum of 100,000 of the species, rewrite your equation from part a.A compostable bag breaks down such that only 10% remains in 6 months.r=38.4% decay per monthIf the decomposition is continual, at what rate is the bag decomposing?21.5% remainingHow much of the bag remained after 4 months?after 12 monthsWhen will there be less than 1% of the bag remaining?A 15’ ladder is rated to have no more than a 70° angle and no less than a 40° angle.11.5 feetWhat is maximum rated distance the ladder can be placed from the wall?14.1 feetHow high up a wall can the ladder reach and be within the acceptable use limits?At what base angle should the ladder be placed to reach 10’ up the wall?41.8° ................
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