Seattle City Light charges residents for electricity on a da

Seattle City Light charges residents for electricity on a daily basis. There is basic daily charge of 15 cents. For each day the first 10 kWh cost 6 cents per kWh and any additional kWhs are 12 cents per kWh. (A kilowatt hour is a unit of energy. For example, a 100 watts lamp operating for 10 hours continuously uses 1 kWh.) Make a table showing the cost in cents of usage from 0 to 40 kWh in increments of 5 kWh. Write a piecewise defined function to describe the cost. C(x) 0 lessthanorequalto x lessthanorequalto 10 10

Solution

a) kWh 0 --- 5 - -----15 ---20 ---- 25 ----30 ----35---- 40

Cost 15 - 15 +30 - 15+60 - 15 +60 +60 - 15 +60 +180 ---- 15+60 + 240 ---15 +60+ 300 ---15 +60 +360

= 15 --- 35 --- 75 -- 135 -- 255 --- 315 --- 375 --435

b) C(x) = 15 + 6x for 0<=x<=10

C(x) = 15 +60 +12x = 75 +12x for x>10

c) C(x) = 15 +6*10 = 75 so, x < 10 KWH

33= 15+6x

6x = 18

x = 3 kWh

d) $3 = 300 cents

for x <10 maximum C(10) = 15 + 10*6 = 75

So, x> 10 ; 300 = 75 +12x

12x = 300 -75

x = 18.75 kWh