& . NO:0 " eriven function t (xx) = + + also given that m = 0 1+1 this function is defined only if denominator vie x ( X +1) ( ith ) to =>1+0, x#-1, >17-4 = 1 # 4 - 1,0 so, domain of t(x) is R - 3'753 =160 3XILT) =10 lacking log on both lides 3- J Jay (375) = Joy (25)"+ dry (x-3) - Jog (3') = Joy (1 ) + dog (01-3) ) = Joy (zx ( 13) ) using the bellow formulas () dot (ab) = loyaldalLet- Pct) be the number of bacteria at time t . Then Pct) = Poe where Po is initial number of bacteria Given Po = 20000 and p(50) = 2Po (a) P ( 50 ) = Do er ( 50 ) 7 2 Po = Poe 50Y 3 2 =0 50Y 3 50r = In(2) - r= =in(2). or er = (2) 1/50 Thus, the model that gives the number of bacteria at time t is . PCt) = 20, 000 (2)50 (b ) when t= 2 25 P (2) = 20,000 (2) = 20,000 (2) = 20, 562 approximatelyThe number of bacteria after two hours is 20, 562 approximately c ) when PCL ) = 90, 000 90,000 = 20,000@ (2) 50 2 = (2) 50 In (9 ) = E . In (2 ) 50 t= 50-10(9/2) 1 108 . 496 In (2 ) There will be 90800 bacteria in the culture after 108 minutes") Step-It Identity the type of Parabola. it "" coefficient positive - open's upward. coefficient reptile ) open's downward. " coefficient it negative .. open's downward. verer of parabola . found in Partla) .) (8, 36) Point where MUSEO . - 0-45 5 45420-0. 52 - 165 - 80 0 5 = +16+ 156 4 320 S = 16 # 24 $= 10 -4 2. 3 (+ 20, 0) 4 (-4,0) Step -4 3 ) coordinate where function meet you's Le S=0. M() = 20 (0, 20) (9, 30) 4 Parabola . (01 20) ( 201 0 ) ( - 7 0 )Solution Given, moo + 43 + 20 a) as the function of mileage is a quadratic equation, it will be a Parabola. will be inveered Papaboin VOreI The maximum voue ofy" is obtained at Vil for Parabela 9= 0x4bitc I - ceadivert of vertt is given by -b MU)= - D.256 445+20 as -0.15, b= 4, C: 20. S = -b 4 0.5 woodmum freed S= 9 milk Substituting 's' in M() M() = - 0-25 (9) 4 4(8) +20 52 - 16 M() = 36 m /04 best mileage s = 8 mi/ h (3, 36) Speed at which best mileage is obtained