<p>For half of you who took the December SAT yesterday, you probably remember a math question (last one of section 2) that asked for average rate of change of pounds of tomatoes per person per year. Well, it seems like nobody got the question (as far as I can tell in the Math thread) and after talking this over with my parents (MBA and Ph.D in Economics), they agree that the wording and answers were rather vaguely worded.</p>
<p>Has petitioning a question ever worked for anybody? Is this even possible for the SAT? I know you can do this for the PSAT, but I can't find anything about petitions for the SAT.</p>
<p>A) 1/4
B) 1/2
C) 2
D) 2 1/2 (2 and a half)
E) 5</p>
<p>Every person I’ve talked to on CC and in person did delta y/delta x and got 1/4 or 1/2, since the question asked for an answer in pounds per person per year. But, my econ/business parents say (and they’re right) that “average rate of change” means a percent. The thing is, there were no percent signs in the answer choices and the wording “in pounds per person per year” implied (at least, IMO) that those were the units of the right answer. I just wonder if this is enough ambiguity to get this question not scored or something.</p>
<p>If the original graph was graphing consumption in “pounds per person” vs “years”, then the average rate of change would be found by taking the slope of the graph from 2 suitable points…thus as you said, delta y over delta x. The units of that slope would be the units of the y quantity divided by the units of the x quantity, so in this case it would be (pounds per person) per year.</p>
<p>(I don’t know what you mean when you say it should have been expressed as a percent. It does not have to be. It COULD be, but in fact ANY number can be expressed as a percent if you feel like it. Nothing about this case requires it.)</p>
<p>You may want to compare this to things you learn in physics. Velocity is slope on a position vs time graph so its units are meters per second. Acceleration is slope on a velocity vs time graph so its units are (meters per second) per second. Whenever you take the rate of change of a rate, you end up with units in the form </p>
<p>(THIS per THAT) per OTHER</p>
<p>If you can tolerate one more example: say your hair grows, typically two inches per month. Then you take a wonder drug and it causes that rate to increase but it takes a long time to act. You might experience a change in the growth rate of .5 inches per month per year. That means that over the course of a year, the rate will increase from 2 inches per month to 2.5 inches per month…</p>
<p>This was probably more than you needed to hear about this…bottom line: doesn’t seem to me like there’s anything wrong with this question.</p>
<p>I think my dad’s point is that “average rate of change in pounds per person per year” means that the answer is not the slope and that it’s the economic equivalent of a growth rate, which is given in percent of original quantity (or something like that).</p>
<p>The fact that “in pounds per person per year” implies a unit and the fact that there weren’t percentage signs in the answer choices could possibly be ambiguous.</p>
<p>^The definition of average rate of change (according to my econ teacher dad) is growth rate which is in percent. So the 2 refers to 2%. Like the growth is 2% per year.</p>
<p>In Economics it might be a percent… not in mathematics though.
Google “Average rate of change”, you will find plenty of results that give no indication of a percent needed.</p>
<p>Yes, I admit, that question confused me a bit at first. </p>
<p>For those of you in calculus, the rate of change = derivative, or slope. So basically, it was asking for the average slope between the two points. The answer was 5/22, which is close to 1/4 (they asked for the closest answer).</p>
<p>Does anybody know a math teacher/SAT tutor? In fact, has anybody come across a question like this before? We can use that as a model to compare this question to.</p>
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