.

 

What is crazy about this problem? It seems straightforward to me. The fourth quarter of the calendar year is roughly day 274 thru day 365. The rate of change of a function is another way of saying the derivative of that function. Do you know how to take the derivative of a function? Then you need to take the average value of the function over that time period. If you don't know what the derivative of a function is, then you could also use a spreadsheet and evaluate the function for all integers t in the range 274 to 365, compute the differences and take the average difference. You could also graph the function and draw the best straight-line fit, and the slope of the line will be the average rate of change.

 

Can you find the demand on the first day of the fourth quarter?

Can you find the demand on the last day of the fourth quarter?

If you know the demand at the end of the quarter and at the beginning of the quarter, can you find the increase/decrease in the demand over that quarter.

The thing I find ambiguous about this question is: are they making a distinction between the following two questions:

"Find the average change of the demand over the fourth quarter" and "Find the average rate of change of the demand over the fourth quarter."

If they truly want a rate of change, then what is the time basis? Are they looking for the average rate of change per day? per quarter? per year?

 

Yes this is what i was having trouble understanding. This website is garbage.

That issue has nothing to do with it being an online tool -- poorly expressed questions on assignments have been around far, far longer than computers.

 

I guess I don't see the ambiguity. I understand what you are saying, but I don't think the question is ambiguous at all.

 

I guess I don't see the ambiguity. I understand what you are saying, but I don't think the question is ambiguous at all.

So if the demand at the beginning of the fourth quarter was 100 units and the demand at the end of the quarter was 150 units, what would you say that the "average rate of change" of demand over the fourth quarter is? The demand changed by 50% over the fourth quarter, but what was the average rate of change of the demand over that period? Since the function gives the demand on a daily basis, should the answer be given in units of "average change per day"? Or should it be an annualized rate?

 

So if the demand at the beginning of the fourth quarter was 100 units and the demand at the end of the quarter was 150 units, what would you say that the "average rate of change" of demand over the fourth quarter is? The demand changed by 50% over the fourth quarter, but what was the average rate of change of the demand over that period? Since the function gives the demand on a daily basis, should the answer be given in units of "average change per day"? Or should it be an annualized rate?

I gave the clue of how to do it in my previous post. Use a spreadsheet to compute the daily demand for days 275 thru 365. Approximate the derivative by making a table of first differences. Take the average of the first differences. If you do this procedure the result is actually quite surprising and doesn't actually require the computation of the average rate of change because the actual rate of change, is by inspection, ________. (Fill in the blank)

The units in this case are "demand change per day"

 

But on what basis can you conclude that the rate they are looking for is per day? And is that rate simple or compounded?

 

You're welcome to over think this, but I don't think the writers are that deep. If it turns out that they truly are that deep -- well I've been wrong before.

The original function is very nearly linear and the rate of change of a linear function is constant. As such the instantaneous rate of change and any average rate of change are going to be proportional to the slope of the function. Any answer that identifies the slope of the function must be correct.

 

You're welcome to over think this, but I don't think the writers are that deep. If it turns out that they truly are that deep -- well I've been wrong before.

The original function is very nearly linear and the rate of change of a linear function is constant. As such the instantaneous rate of change and any average rate of change are going to be proportional to the slope of the function. Any answer that identifies the slope of the function must be correct.

That last sentence is right at the heart of the matter. If grading manually, then any answer that identifies the slope of the function should be considered correct, or at least given serious partial credit (I would say full credit to allow for reasonable interpretation of the time basis and the compounding question, which really come down to how the material was presented). But with it being an online autograded assignment, anything that is not within the tolerance of the exact interpretation the writer had in mind will simply be marked incorrect. While it is possible with most of these systems to override the grade manually, it is a royal pain in most of them. Worse, the confusion and frustration that the student endures can be excessive. Most systems allow you to add hints that are given out each time a wrong answer is submitted, which can be very helpful and, in my opinion, are the big strength of these systems; but setting those up is extremely time consuming and setting up good hints is extremely difficult, much more so than it would seem like it should be, because you have to set them up blind beforehand as opposed to having them be in response to what the student actually did. Some systems are adaptive and give different hints based on the submitted answer, but those are even harder to set up well and the submitted answer may or may not map to the assumed error that the student made for the hint given.

 

My 2¢. I would take for granted that time is to be expressed in days, since that is given in the problem. It's an assumption, but that's the way tests are.

The problem I have is that the question specifically asks for ONE thing, the average slope over the 4th quarter, but then there are two spots for entering answers. One appears to be a multiple choice pulldown to show demand for the entire quarter, although that's a guess also.

 

My 2¢. I would take for granted that time is to be expressed in days, since that is given in the problem. It's an assumption, but that's the way tests are.

The problem I have is that the question specifically asks for ONE thing, the average slope over the 4th quarter, but then there are two spots for entering answers. One appears to be a multiple choice pulldown to show demand for the entire quarter, although that's a guess also.

The first answer is just to select whether it is increasing or decreasing and the second one is to enter the (absolute value of the) rate.

 

@Ripneumann We are basically waiting for you to come back with any further assistance you need. If you still aren't getting the right answer, show us what you are doing and we can offer some suggestions. In the meantime, we are operating open-loop and just meandering.

 

The first answer is just to select whether it is increasing or decreasing and the second one is to enter the (absolute value of the) rate.

Ah, yes, I see that now. My bad. This would be apparent to the person answering online.

In that case, I'm with PB and see little to complain about.

I know you'll agree that the teacher is doing a disservice by asking for an answer devoid of units. A good teacher would instill in the student to ALWAYS start with the units and only then proceed to a numerical answer. This type of question teaches them to be sloppy.

 

Ah, yes, I see that now. My bad. This would be apparent to the person answering online.

In that case, I'm with PB and see little to complain about.

I know you'll agree that the teacher is doing a disservice by asking for an answer devoid of units. A good teacher would instill in the student to ALWAYS start with the units and only then proceed to a numerical answer. This type of question teaches them to be sloppy.

I agree. Some of the online systems support units, meaning that the student determines the units and includes that as part of their answer. The system is smart enough to convert from compatible units that are reasonably close to the units that the encoded answer is given in. But it has been my (limited) experience that these systems still fall well short of being robust enough to be really useful. Still, at least some developers are giving the matter the attention it deserves.

 

The question doesn't make sense.

Average is a concept for discrete math. Rate of change (1st order derivative) is not.

The closest equivalent to "average" here is integration.

So Average (d d(t) / dt) = integration (d d(t) / dt) over Q3 -> Q4 = (d(365) - d(250)) / (365 - 250) = ...

Essentially, the average demand in Q4.

 

Average is not a concept that is limited to discrete math.

For this question, the average that it is looking for is NOT the average demand, it is the average rate of change of the demand.

 

The use of the word average in this question is a complete red herring. For a linear function the instantaneous rate of change and any notion of average rate of change are exactly the same thing -- a constant!