Question

2. A solar lease customer built up an excess of 6,500 kilowatt hours (kwh) during the summer using his solar

panels. When he turned his electric heat on, the excess began to be used up at a rate of 50 kilowatt hours
per day.
(a) If E represents the excess left and d represents (b) How much of the excess will be left after one
the number of days since the heat has been month (use a month length of 30 days)?
turned on, write an equation for E in terms of d.
(c) If the heat will need to be turned on for 5 months, will the excess be enough to last through this time
period? Justify your answer.

Answer 1

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Answer:

a) E = 6500 -50d

b) 5000 kWh

c) the excess will last only 130 days, not enough for 5 months

Explanation:

Given:

starting excess (E): 6500 kWh

usage: 50 kWh/day (d)

Find:

a) E(d)

b) E(30)

c) E(150)

Solution:

a) The exces is linearly decreasing with the number of days, so we have ...

E(d) = 6500 -50d

__

b) After 30 days, the excess remaining is ...

E(30) = 6500 -50(30) = 5000 . . . . kWh after 30 days

__

c) After 150 days, the excess remaining would be ...

E(150) = 6500 -50(150) = 6500 -7500 = -1000 . . . . 150 days is beyond the capacity of the system

The supply is not enough to last for 5 months.