A utility company expects consumption of electricity to increase by 8% in the next decade.?

Question

Find the amount by which the utility company will have increase its generating capasity.

I think that I should be using the interst rate formula P(1+rt) but the question does not give any more info than what I have listed.

this is from a business calculus course. This chapter is on compound interest. If you can give me info on how you came to your answers I would be very grateful. I like answers but I like understanding them better.

There is no more information. That is why this question is so frustrating.

Answer 1

The question did not say 8% annually. I take it to mean 8% over the next ten years.

Demand * .08 = Increase in generating capacity.

Demand * 1.08 = Next decade's demand


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If the question intended an annual load growth of 8%, then the formula is the one used for compounding interest.

(1 + r)^t
r = interest rate (or in this case, growth rate)
t = time, a.k.a. compounding intervals (in this case, 10 years)

(1.08)^10 = 2.16

The future generating capacity will have to be 216% of today's capacity. They already have a certain amount of existing generating capacity, so they will need to add another 116%.

Your equation is close, but it is F = P(1+r)^t
F = future value
P = present value
r = growth rate
t = time
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I might be splitting hairs here, but there is a difference between consumption and generating capacity.

Consumption is the energy that are used each year. Generating capacity is needed to meet the peak day demand requirements. Depending on the usage patterns, the utility might not need to add more generating capacity.

Think of it this way: In the next decade you will drive 8% more. Does this mean you are going to buy an additional car? No, it just means you're going to be driving more miles. with the car you already have.

Answer 2

Why wouldn't they just have to increase the generating capacity by 8% by the end of the decade???? It seems simple enough. In other words, it answers itself.

Perhaps there is something else to it. For example, did the question state what period over which they must increase their capacity, such as over a year? And what about conservation? If they could simply get their customers to consume 8% less electricity over the next decade, they wouldn't have to increase the generating capacity at all. (Already there are laws requiring electric companies to make concerted efforts to reduce consumption before they would even be allowed to build more plant, in which case the question could be mute.)

If I got a question like that from a school, I would be all over them like stink on, uh... burned out generators.

Answer 3

Clearly they mean 8% annually, so you need to apply the compound interest formula.

There are so many assumptions you have to make that it's almost comical, but here goes.

Assume that the power company is already at maximum capacity at the current consumption and assume that they don't need to provide any cushion. Let C equal the current capacity of the company, it will need to be C(1+.08)^10 in ten years, or 2.16C. So, they will need to increase their capacity by 216%

Answer 4

108%