Question

[10 marks) 5. An electricity company charges its customers a base rate of $15 a month plus 8 cents per kilowatt-hour (kWh) for the first 1200 kWh and 12 cents per kWh for usage over 1200 kWh. Write the cost, C, in dollars as a function of x, the number of kWh used for 05x< 1500 and graph the function [8 marks] 6. A certain paper book sells for $25. The author receives a royalty of 12% on the first 5000 copies sold, 15% on the next 10000 copies sold, and 20% for any additional copies sold. Write R, the amount of royalties in dollars as a function of x, the number of copies sold. [12 marks] 5x+2 (4 marks) (4 marks) (4 marks) 7. For the function f(x) a. Show that it is one-to-one. b. Find the inverse, f-(). c. Check that f(-'(x)) = x. (10 marks 1000 (4 marks) 8. Suppose that the population of a certain species is given by P(t) = where t is given in years. a. Find the inverse of P. b. Use the inverse in a. to find the time required for the population to reach 800. c. What happens to the population as time goes on, i.e. as (4 marks) (2 marks)

Answer 1

Ang 5] There is a monthly charge of $15 fixed, even it there is no consumption There will be charge of $0.08 per kwn consumed upto 1200 kWh Total monthly charge is E= 15+0.0882 at in the amount of Electricity consumed during the menth in kWh E= $15+0.08xx when as 1200 kWh Energy Coat for the tirst 1200 kWh E1200-$15 +0.08x1200 = $ 111 For consumption over 1200 kWh the cost wiu be E>1200 = 0.12X(24-1200) Remember this termula must be applied for any consumption over 1200 kwh, that is why the rate $0.12 de multiplied by 12-1200) E= $111+ 0012(x-1200) tox &> 1200kwh. The monthly coat E as a tunction of the amount of Euchcity consumed is E- $15+0.08x* ter ></200 E = $111 +0012(31-1200) tor 21200 → Slepe = 0.12 (1200,111) Slope =0008

100 Ans) → pt n $ 5000 R=12 X25XX 100 R=3x → it 5000 * 310000 REIS x 25 x (31-5000) + 12 X 25 X 5000 100 100 = 15000 +15 (71-5000) R = 154 4 1t >>10,000 R: 12 x 25X 5000 +15x25x(10000-5000) +20 x25x1*-10000 100 15000 4 1 Too = 15000 + 18 750 +521 - 50000 R = 5x-16250

Ans) f(x) = - UDL S4+2 The wroph of the wire is :- (a) Therefore, to the graph of F(X) We can see that f(21) has disserent Values tor tHE Domain, theretose it is one to one. (b) y = - 41 4+2 to tind F-1(20 replace a with y and y with x = - 44 Sy+2 504+2x=-44 514 tyy=-2x y (4+52)=-22 y=-22 4+52 IF-1(+1)= - 2x 4+5X F(F"(x) = -4 () slim) B4 --> 821 4450 -Loxton+8 4457 8 1+2 Thereture, HF-1(31) = x, fs Toue,

Ans P(): looo It get + Choose 1000 1+30) It gey = 1000 t gey - (1000) et (1964) e (a) f(t)= y = - An( lage 4)) 0 (6) t=305835 Put t=800 in eq @ (C2 em 1000 It get = 1000