Question

16. The population of an endangered species of turtles will grow according to the model: 500 1+83e-0.1620 P(t) (a)Setermine the carrying capacity (b)The growth rate of the turtle (c)The population after 3 years (d) When will the pop[ulation reach 300 turtles 17. A thermometer reading 72°F is placed in a refrigerator where the temperature is a constant 38 (a)lf the thermometer reads 60°F after 2mins.what will it read after 7 minutes? (b) How long will it take before the thermometer reads 39°F? 18. For the parabola: (x + 4)2 = 16(y + 2) find (a)the vertex (b) the focus (C) the directrix (x-3) 19. For the ellipse: + (y+1) 9 = 1 find 4 (a)the center 9b) the vertices (C)the foci (d)its orientation 20. For the hyperbola: (x-2) (+3) = 1 find 4 9 (a) the center (b)the transverse axis (C)the vertices (d)the foci (e)its orientation

Answer 1

16 500 PCH) 1+ 83e-0.1626 @ when too P (t) & 500 and to the eanying Capicity is 500, b -0.1627 de 500 X 83x 0.162 e (1483 1 +832-0.1627 j 6#23 xe-o. 16 (L* 83 e-0.1824) e which is the nate growth the tuntle, of 5070 500 9.6 P(3) 1483 e 0.162X3 14 51.05 ~ 10. I Let after t time the population beach at 300 PA) = 800 = 300 1483e- 0.1627 0.1627 sro Zoo V If 83e > 83 2-0.1627 2/3 0.1627 83X3 2 - e white " to ta loge @42) = 29.77 30 years 0.162 ( 17 sinformation missing :) mitting / incomplete.

(13 * (***) *= 16 (981) (x+y) Euxu (2+2) (4,2) 배 The vented is (-4,-2) (-4,-2). b Co-ordinate of focus (-4,4-2) =(4,2) are The panabala is eepwand direction with axis parallel to y axis. The equation of axisi's 2+4=O. The directrix is y tu +4 = -2 =) => y =-6 (19 - 3)2 (1) * + - 4 # (3,2) conture of ellipse is (3,-1) b The ventices are A for food and ! we neunite the equation as Gead)" (7-812 Y 01 13,-4) =1 62 az

then as 3, p= -1, Q59, b=2, A (, a+p) A(3, 3-1) = A ( 3,2) A' (2, -a +iB) Al (3,-9-1) W! (3,-4) ale know that the ene (a, the co-ondinates of foci I ae) cuhene Ver in blar ß: es Ir (43) 9-4 rs/5. : F (3,-1+rs) and F' (S-1-13). D The ellipse is vertical whose maton axis is Parallel to os axis and minor axis is parallel to a axis. The length of Serra majon axis = 3: M minov n 2. (20 "رومن) (2-2) following form, comparing the above equation in the fa-an (y-B)? then me get, Ĉl b2 de 2, b=3 a=2, Bs-3 @ the center of hyperbola is baya) = (2,-3).

bi The transverse ax's is 8+3=0. le The ventices are (2,-3) (eta, A) = (2+2, -3) ie (0-3) and (4,-3) d @ The hyperbola is such that is transverse axis is Parallel to a i's a axis and conjugate axis panallel to y axes,