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Q&A #251

Teachers' Lounge Discussion: New examples of growth in calculus

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From: RON

To: Teacher2Teacher Public Discussion
Date: 2003050621:50:17
Subject: NEW EXAMPLES OF GROWTH IN CALCULUS

FOR GROWTH/DECAY EXAMPLES, I SUGGEST THE FOLLOWING: 1) RADIO CARBON DATING TESTING OF THE SHROUD OF TURIN FOR TIME OF ORIGIN. THE TOPIC MAY POSSIBLY NOT BE APPROPRIATE DEPENDING UPON YOUR COMMUNITY, BUT THE SCIENCE IS OFFERED AS EVIDENCE TO HELP SOLVE A RELIGIOUS MYSTERY. BASIC DECAY FORMULAS CAN BE OBTAINED FROM MOST TEXTS. 2) EXPLORE THE NEW WAVE OF MATH INTEREST IN THE STOCK MARKET. SEVERAL YEARS AGO THE NOBEL PRIZE IN ECONOMICS WAS AWARDED TO PEOPLE WHO WERE TRYING TO PREDICT THE VALUE OF DERIVATIVES. THE FORMULA INVOLVING EULER'S NUMBER CAN BE SEEN ALONG WITH AN ARTICLE AT www.nobel.se/economics/laureates/1997/back.html 3) ON THE MORE AMUSING SIDE, I ONCE USED A REAL LIFE MISHAP FOR A PROBLEM. THE BIOLOGY DEPT. WAS CONDUCTING FRUIT FLY EXPERIMENTS IN GENETICS. ONE DISGRUNTLED STUDENT DECIDED TO "FREE THE FRUIT FLIES" BY TAKING OUT THE COTTON STOPPERS FROM THE TEST TUBES. AN ENTIRE WING OF THE BUILDING WAS INFESTED FOR QUITE SOME TIME. I USED TO COME INTO WORK IN THE MORNING AND NOTE SEVERAL ESCAPEES SORT OF BOUNCING ACROSS MY DESK. A FEW MADE UP INITIAL CONDITION NUMBERS LATER, AND I HAD AN EXPONENTIAL GROWTH PROBLEM FOR MY STUDENTS. 4) AS FOR TRIGONOMETRIC GROWTH/DECAY, THAT IS A TOUGH ONE. I SEEM TO RECALL THAT WHEN THERE WAS A RABBIT POPULATION PROBLEM A FEW YEARS AGO ON SOME ISLAND ( MAYBE IN MICHIGAN OR MINNESOTA?). THE SOLUTION USED WAS TO INTRODUCE WOLVES ONTO THE ISLAND. THE RESULTING POPULATIONS OF RABBITS AND WOLVES BEHAVED SOMEWHAT SINUSOIDALLY. AS EXPECTED, AS THE WOLVES ATE RABBITS, THE FOOD SOURCE BECAME MORE SCARCE AND AS A RESULT THE POPULATION OF THE WOLVES NATURALLY DECREASED. WITH FEWER WOLVES, THE RABBITS WERE ABLE TO BOUNCE BACK TO LARGER POPULATIONS. WITH MORE FOOD AVAILABLE, BACK CAME THE WOLF POPULATION, AND SO ON AND SO ON. THE RESULTING EVENTUAL EQUILIBRIUM WAS BASICALLY LIKE OUT OF PHASE SINE WAVES FOR BOTH POPULATIONS.

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