Question

p(t) hundred dollars per year p(t) = 0.6677-1212 +40t +80 gives the rate of change of profit (in hundred dollars per year) at Java Joe's, t years after 2000, 0 SI 512. Check: p(4)=90.688 Use this information to answer the next six questions. 8 9 10 11 12

Answer 1

Given that, Ane pet) = 0.667 83 12t² t got + 80 giver the rate of change of profit Cin hundred dollare per year 'ť year e afted 2000 , Ostfla ) وحدہ (ث plet) = qt'-24++40 20 act²-12t+20) = 0 £²_12t +20=0 t² cok-at +2020 >> *(4-0)-267-10770 5 (7-2) ct-2020 t = 2, t=10 at .. Coritical point & PICT). 4 t - 24 tad, pl(®)=8-04:-1610 porofit is higher in Joootd : din from 2005 to 2010, ļ70.66773-12+ + 406 +80) dt Qool // 5

= 60.4874+ 4+ 120*48047" Com 0.642 (1039 401+200103 780 »] - [ 00967 (5)*-400+201597801537 +80 (10) 467.5 - 504.219 36.719. protit decoleaged by 36.719 hundred doves A(X). Plt) dt 0 = Alca)= P(a) f'(x) = pin) = 0.6674?_1&ty 40t +86-0 four colitical point +0.66729-122°740x +8030 ,by calculatoor (ocn212) + X = 7.022 7.022 12 flon) decreasing on the interval (0,7.001). since 7.022 is corifical point . so, Ala) decacasing at slow gate neas 7.odel:

tve -Ve twee at Mo, f(x) i es decreasing a slower rate 32426.,, Cår) All (X) = 2X2-24x + 40 =0 =21x2-12x720)-6 1=2,10 Now Sign Macle A cole 40 1(3): 18-72+40= -14 +" (119=2922-269+ 40 = 18 tive. Between 2 and 10 sign nega down Qr4010).. 12) Spct) at A is Therge-fore concave وہ ( م و پیشہ ور بومه ال dt 2 0.667 +4, 4+*+20+' 7804 +c 4 > 10)-500 soo o ototote => C-500 A(X)= 0.667+2 4+*+20+2 +807 +500 A(2) = 0.667 (16) - 418) +20 (4) + 80 (2) +500

710.7 $710.7 i) Psigned appea =60.6677?. 4 tºtxotikot 386 12 Total area 7 +(10:0017 12 pct) at + 1lf pct at / (0.667+*_14°420tº7804) ***t voti sot 17 - (0.642 (734- 4112+20013780(1)] + 116 0:$67(1232411232420023 48002)) – (0.467 007 4/132 2001378061)|| 568.366 + 1/ 386 568.366) 568.366+182.366 = 750.732 © 751 lege foole, The total signed area between P(E) and * - Qarie 386). And, the total area bleo pct) & t-anie 921751 386, 75) please "Upvote", Thank you, tlence solved l