Bl Theraja Vol 4 Pdf
Karri Weston
Long ago in India, there lived a raja who believedhe was wise and fair, as a raja should be. The people in his provincewere rice farmers. The raja decreed that everyone must give nearlyall of their rice to him. "I will store the rice safely,"the raja promised the people, "so that in time of famine,everyone will have rice to eat, and no one will go hungry."Each year, the raja's rice collectors gathered nearly all of thepeople's rice and carried it away to the royal storehouses.
For many years, the rice grew well. The peoplegave nearly all of their rice to the raja, and the storehouseswere always full. But the people were left with only enough riceto get by. Then one year the rice grew badly and there was famineand hunger. The people had no rice to give to the raja, and theyhad no rice to eat. The raja's ministers implored him, "Yourhighness, let us open the royal storehouses and give the riceto the people, as you promised." "No!" cried theraja. How do I know how long the famine will last? I must havethe rice for myself. Promis or no promise, a raja must not gohungry!"
Time went on, and the people grew more andmore hungry. But the raja would not give out the rice. One day,the raja ordered a feast for himself and his court--as, it seemedto him, a raja should now and then, even when there is famine.A servant led an elephant from a royal storehouse to the palace,carrying two full baskets of rice. A village girl named Rani sawthat a trickle of rice was falling from one of the baskets. Quicklyshe jumped up and walked along beside the elephant, catching thefalling rice in her skirt. She was clever, and she began to makea plan.
"Very well," said Rani. "Ifit pleased Your Highness, you may reward me in this way. Today,you will give me a single grain of rice. Then, each day for thirtydays you will give me double the rice you gave me the day before.Thus, tomorrow you will give me two grains of rice, the next dayfour grains of rice, and so on for thirty day."
Now, it is the student's job to build a spreadsheetbased upon this story to determine the amount of rice given toRani on any given day. We start the spreadsheet by listing underthe heading, "day," 1....30. Then we proceed with thefollowing formula: 2*(previous cell address) and fill down. Aftereach day, read the part of the story that corresponds to thatday. (Read the number AFTER they find it using the spreadsheet)
On the ninth day, Rani was presented with twohundred fifty-six grains of rice. She had received in all fivehundred and eleven grains of rice, enough for only a small handful."This girl is honest, but not very clever," thoughtthe raja. "She would have gained more rice by keeping whatfell into her skirt!"
On the sixteenth day, Rani was presented witha bag containing thirty-two thousand, seven hundred and sixty-eightgrains of rice. All together she had enough rice for two bags."This doubling up adds up to more rice than I expected"thought the raja. "But surely her reward won't amount tomuch more."
On the twenty-fourth day, Rani was presentedwith eight million, three hundred and eighty-eight thousand, sixhundred and eight grains of rice--enough to fill eight baskets,which were carried to her by eight royal deer.
On the twenty-seventh day, thirty-two brahmabulls were needed to deliver sixty-four baskets of rice. The rajawas deeply troubled. "One grain of rice has grown very greatindeed," he thought. "But I shall fulfill the rewardto the end, as a raja should."
On the thirtieth and final day, two hundredand fifty-six elephants crossed the province, carrying the contentsof the last four royal storehouses--Five hundred and thirty-sixmillion, eight hundred and seventy thousand, nine hundred andtwelve grains of rice.
Now, have the students add the columns to seehow many grains of rice Rani received in all. Have the studentsgraph this relation with Excel. Days = x, grains of rice = y.Ask them if it is a function. Explain that it is an exponentialfunction.
Extension for calculus students: what is the significance of the cumulative amountof rice Rani has received on any given day? Answer: area underthe curve. Have them calculate the area over different intervalsto check.
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