creekland Posted March 24, 2011 Share Posted March 24, 2011 If your student is in or has done Pre-Calc, would they know how to create an exponential function from two points? In other words, if you gave them the points (4, 20) and (6, 80) would they be able to create an exponential function with no other details? I know how to do the math (I showed kids how today at school), but I seriously haven't seen this come up at all since college - not even in the 11 years I've been subbing at this school (it was a new question just added to a chapter test in Pre-Calc this year - none of the kids could answer it). It may or may not have been in their book. I didn't look at it. I'm not asking "how" to do it. I'm just wondering if other books teach it and that's why it was added? Was there some "need" our school saw? I don't always supervise my own kids' math, so I honestly don't know yet if middle son could do it or not. I plan to ask him at some point. He's not home tonight and is leaving tomorrow for a weekend trip. Meanwhile, I'm curious and it's gnawing at me. If you ask college students, be sure to ask which course they learned it in if they know how. It wouldn't surprise me at all to find it in a college class. I'm mainly curious if it's in other Pre-Calc books. I seriously don't remember learning it in high school (and I went to a VERY good high school), but that was many moons ago and I'll never claim I have perfect memory. :tongue_smilie: Sometimes I wonder why these things stay on my mind anyway, but that's a whole 'nother issue. Songs anyone? Row, row, row your boat, gently down the stream... Quote Link to comment Share on other sites More sharing options...
Caroline Posted March 25, 2011 Share Posted March 25, 2011 I teach it in Math 3, which is the algebra 2 equivalent in Georgia. I also revisit it when I teach separable differential equations in AP Calculus AB. Quote Link to comment Share on other sites More sharing options...
regentrude Posted March 25, 2011 Share Posted March 25, 2011 Stupid question: when you say "exponential function from two points", are you talking about y=a b^x (find a and b, i.e. the base) or y= c e^(kx) (find C and k, i.e. a factor in the exponent)? Thanks! Quote Link to comment Share on other sites More sharing options...
creekland Posted March 25, 2011 Author Share Posted March 25, 2011 I teach it in Math 3, which is the algebra 2 equivalent in Georgia. I also revisit it when I teach separable differential equations in AP Calculus AB. Thanks. It would make more sense to teach it in Alg 2 IMO. It MIGHT be in the Alg 2 book at school, but once again, our school only covers the first half of the course and grants a whole credit for it. There were some VERY talented math kids in my classes today, so I was super surprised when no one got the answer (no one even came close). They weren't pleased, so I showed them how it was done after the test. If it's on a test... one would think it had been covered in class... and one would think it had been taught... and one would think at least some of the talented kids would have gotten it since it's a rather easy one. Ok, MY brain has figured out MY reason for wanting to know. My youngest is at this school. Am I looking at a book/curriculum I already know I can't stand and will need to watch out for (in this section) or am I looking at a teacher I want to have my kid avoid... or both. I don't mind supplementing when I know what I have to supplement. I won't be happy supplementing AFTER a grade is on the books for something beyond their control. Quote Link to comment Share on other sites More sharing options...
creekland Posted March 25, 2011 Author Share Posted March 25, 2011 Stupid question: when you say "exponential function from two points", are you talking about y=a b^x (find a and b, i.e. the base) or y= c e^(kx) (find C and k, i.e. a factor in the exponent)?Thanks! Good question. I showed them the first as it's what came to mind. I didn't have an answer key, so now I'm wondering if he wanted the second. The question was worded on the test exactly as I worded it. (Create an exponential function from these two points (4, 20) and (6,80). Is it increasing or decreasing?) The kids were allowed a "cheat sheet" of their own making for the test. None of the kids had anything even remotely similar to it on their cheat sheets - at least - not those that I briefly looked at. Quote Link to comment Share on other sites More sharing options...
KAR120C Posted March 25, 2011 Share Posted March 25, 2011 If your student is in or has done Pre-Calc, would they know how to create an exponential function from two points? The tutoring kid I have in Precalc right now might not remember it off the top of his head (being up to his eyeballs in trig right now...), but I think he could hack his way through. Quote Link to comment Share on other sites More sharing options...
creekland Posted March 25, 2011 Author Share Posted March 25, 2011 The tutoring kid I have in Precalc right now might not remember it off the top of his head (being up to his eyeballs in trig right now...), but I think he could hack his way through. So likely learned in Alg 2? This could be why I missed it in high school. NY, when I was in high school, had a Math 1, Math 2, and Math 3 system. I skipped Math 3 as I was in FL that year (10th grade) and took Trig/Analytic Geometry down there. I took the Math 3 Regents when I returned home to keep my NY regents diploma going, but it wasn't likely to have been on that test I suspect. Or again, it might have been and my brain is just fuzzy as to exactly when I learned it since I haven't seen it in eons. The next song playing in my head? Memories... ;) But I digress. And I wonder why our school falls below average in our state and in college testing for math. BUT, that may be why it was added. Now if it were to be TAUGHT before they are tested on it. One has to feel sorry for the kids sometimes. Quote Link to comment Share on other sites More sharing options...
Teachin'Mine Posted March 25, 2011 Share Posted March 25, 2011 (edited) nm : ) Edited March 25, 2011 by Teachin'Mine Quote Link to comment Share on other sites More sharing options...
KAR120C Posted March 25, 2011 Share Posted March 25, 2011 So likely learned in Alg 2? (Assuming you do mean y=ab^x...) We did all things exponential and logarithmic in Algebra 2. Okay not ALL things, but all the basics. Quote Link to comment Share on other sites More sharing options...
creekland Posted March 25, 2011 Author Share Posted March 25, 2011 (Assuming you do mean y=ab^x...) We did all things exponential and logarithmic in Algebra 2. Okay not ALL things, but all the basics. Logs are Pre-Calc at our school. This test also covered other log functions. So maybe it is in this section. Logs had been dropped almost completely until recently or put at the end of the year after grades were in (when kids really didn't care to absorb anything), so it would go with the trend of bringing some things back - probably due to state tests. I'm trying to get them to add circles back into geometry too. They are needed on the SAT/ACT as well as in other math classes. I've been pointing that out to powers that be. The problem is (they say) what else would I have them cut? Block scheduling does not work with math - esp when so many teaching days are lost due to testing, movie days, snow delays, and other such things. Quote Link to comment Share on other sites More sharing options...
KAR120C Posted March 25, 2011 Share Posted March 25, 2011 Logs are Pre-Calc at our school. This test also covered other log functions. So maybe it is in this section. Logs had been dropped almost completely until recently or put at the end of the year after grades were in (when kids really didn't care to absorb anything), so it would go with the trend of bringing some things back - probably due to state tests. I'm trying to get them to add circles back into geometry too. They are needed on the SAT/ACT as well as in other math classes. I've been pointing that out to powers that be. The problem is (they say) what else would I have them cut? Block scheduling does not work with math - esp when so many teaching days are lost due to testing, movie days, snow delays, and other such things. No circles in geometry?? Wow... I'm not a fan of block scheduling anyway, but if it means no circles... I don't think it's really a whole geometry course! Yikes. Logs have to be in Algebra 2 (in my little world LOL) because Algebra 2 is the only prerequisite for AP Stats... and you need to know about exponents and logs to do the logarithmic translation of exponential data to a nice line that you can do a linear regression on.... At least that's the speech I gave the tutoring kid when we got to that chapter last year. LOL Quote Link to comment Share on other sites More sharing options...
creekland Posted March 25, 2011 Author Share Posted March 25, 2011 No circles in geometry?? Wow... I'm not a fan of block scheduling anyway, but if it means no circles... I don't think it's really a whole geometry course! Yikes. Logs have to be in Algebra 2 (in my little world LOL) because Algebra 2 is the only prerequisite for AP Stats... and you need to know about exponents and logs to do the logarithmic translation of exponential data to a nice line that you can do a linear regression on.... At least that's the speech I gave the tutoring kid when we got to that chapter last year. LOL You make me laugh to think this would be covered in our ps... Hubby and I were discussing it about a month or so ago. Our school doesn't even own any log or half log graph paper. Whether they do it on their calculators in stats or not I'm not certain, but I haven't seen it when I've been in there. They do linear regressions on their calculators, but I don't know if they know what that MEANS. I didn't have to worry about middle son. He just came home and solved the problem easily in under a minute. He didn't remember having to ever do it before, but figured it out easily from what he knew about exponential functions. He was a little creative in how he did it. He took 80=ab^6 and divided both sides by b^2 to get b^4 = 80/ab^2, then substituted that into the other equation to solve for b. I showed him the easier way, but I really admire that he could figure it out by deriving it from a method he knew. It's youngest I'll have to worry about when he gets to Pre-Calc. And yes, he knows he'll be learning about circles (and anything else not covered) to finish his geometry course. There are many things not covered in our school due to lack of time, yet full credit is given for each course. Then, many kids struggle when they get to higher classes in high school and college. Wonder why? Quote Link to comment Share on other sites More sharing options...
KAR120C Posted March 25, 2011 Share Posted March 25, 2011 There are many things not covered in our school due to lack of time, yet full credit is given for each course. Then, many kids struggle when they get to higher classes in high school and college. Wonder why? Don't tell tutoring kid... he already thinks I'm a meanie for making him do a (little) linear regression by hand before I'd let him use the calculator! :tongue_smilie: Quote Link to comment Share on other sites More sharing options...
annabanana1992 Posted March 25, 2011 Share Posted March 25, 2011 I just finished teaching (and testing) this skill in Foerester's Algebra II..... Quote Link to comment Share on other sites More sharing options...
creekland Posted March 25, 2011 Author Share Posted March 25, 2011 I just finished teaching (and testing) this skill in Foerester's Algebra II..... Thanks. I'm suspecting this is a concept being added back into our curriculum and they'll get the kinks out (I hope) by realizing none of the kids knew how to do it. I imagine they'll throw the question off that test, and perhaps, retest it later once they teach it. I could be wrong... My memory is getting fuzzier as I get older, but I'm going to try to make sure I remember this when youngest reaches Pre-Calc and logs. Since he's somewhat on the Aspie side, he'll be furious if he sees something on a test that he hadn't seen before. He doesn't have the math mind to figure it out like middle son did, at least I don't think he could. He possibly could surprise me too as his brain is maturing. I'd rather remember than test it. Quote Link to comment Share on other sites More sharing options...
Caroline Posted March 25, 2011 Share Posted March 25, 2011 Stupid question: when you say "exponential function from two points", are you talking about y=a b^x (find a and b, i.e. the base) or y= c e^(kx) (find C and k, i.e. a factor in the exponent)?Thanks! I teach these simultaneously. Quote Link to comment Share on other sites More sharing options...
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