QUESTION 1 Find an exponential growth model ,N, that represents doubling the rice grains, QUESTION 2 Find a growth model that represents the linear growth, y, of adding two grains of rice, x, every day. QUESTION 3 Provide a sketch of a graph of both the exponential growth and the linear growth on the same set of axes. Attach File Browse My Computer Browse Content Collection "Very well," said Rani. "If it pleases Your Highness, you may reward me in this way. Today, you will give me a single grain of rice. Then, each day for thirty days 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 day four grains of rice, and so on for thirty days." "This seems to be a modest reward," said the raja. "But you shall have it." And Rani was presented with a single grain of rice. The next day, Rani was presented with two grains of rice. And the following day, Rani was presented with four grains of rice. On the ninth day, Rani was presented with two hundred fifty-six grains of rice. She had received in all five hundred and eleven grains of rice, enough for only a small handful. "This girl is honest, but not very clever," thought the raja. "She would have gained more rice by keeping what fell into her skirt!" On the twelfth day, Rani received two thousand and forty-eight grains of rice, about four handfuls. On the thirteenth day, she received four thousand and ninety-six grains of rice, enough to fill a bowl. On the sixteenth day, Rani was presented with a bag containing thirty-two thousand, seven hundred and sixty-eight grains of rice. All together she had enough rice for two bags. "This doubling adds up to more rice than I expected" thought the raja. "But surely her reward won't amount to much more." On the twentieth day, Rani was presented with sixteen more bags filled with rice. On the twenty-first day, she received one million, forty-eight thousand, five hundred seventy-six grains of rice, enough to fill a basket. On the twenty-fourth day, Rani was presented with eight million, three hundred and eighty-eight thousand, six hundred 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 brahma bulls were needed to deliver sixty-four baskets of rice. The raja was deeply troubled. "One grain of rice has grown very great indeed," he thought. "But I shall fulfill the reward to the end, as a raja should." On the twenty-ninth day, Rani was presented with the contents of two royal storehouses. On the thirtieth and final day, two hundred and fifty-six elephants crossed the province, carrying the contents of the last four royal storehouses-- Five hundred and thirty-six million, eight hundred and seventy thousand, nine hundred and twelve grains of rice. Altogether, Rani had received more than one billion grains of rice. The raja had no more rice to give. "And what will you do with this rice," said the raja with a sigh, "now that I have none?" "I shall give it to all the hungry people," said Rani, "and I shall leave a basket of rice for you, too, if you promise from now on to take only as much rice as you need." "I promise," said the raja. And for the rest of his days, the raja was truly wise and fair, as a raja should be. QUESTION 1 Find an exponential growth model ,N, that represents doubling the rice grains, QUESTION 2 Find a growth model that represents the linear growth, y, of adding two grains of rice, x, every day. QUESTION 3 Provide a sketch of a graph of both the exponential growth and the linear growth on the same set of axes. Attach File Browse My Computer Browse Content Collection "Very well," said Rani. "If it pleases Your Highness, you may reward me in this way. Today, you will give me a single grain of rice. Then, each day for thirty days 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 day four grains of rice, and so on for thirty days." "This seems to be a modest reward," said the raja. "But you shall have it." And Rani was presented with a single grain of rice. The next day, Rani was presented with two grains of rice. And the following day, Rani was presented with four grains of rice. On the ninth day, Rani was presented with two hundred fifty-six grains of rice. She had received in all five hundred and eleven grains of rice, enough for only a small handful. "This girl is honest, but not very clever," thought the raja. "She would have gained more rice by keeping what fell into her skirt!" On the twelfth day, Rani received two thousand and forty-eight grains of rice, about four handfuls. On the thirteenth day, she received four thousand and ninety-six grains of rice, enough to fill a bowl. On the sixteenth day, Rani was presented with a bag containing thirty-two thousand, seven hundred and sixty-eight grains of rice. All together she had enough rice for two bags. "This doubling adds up to more rice than I expected" thought the raja. "But surely her reward won't amount to much more." On the twentieth day, Rani was presented with sixteen more bags filled with rice. On the twenty-first day, she received one million, forty-eight thousand, five hundred seventy-six grains of rice, enough to fill a basket. On the twenty-fourth day, Rani was presented with eight million, three hundred and eighty-eight thousand, six hundred 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 brahma bulls were needed to deliver sixty-four baskets of rice. The raja was deeply troubled. "One grain of rice has grown very great indeed," he thought. "But I shall fulfill the reward to the end, as a raja should." On the twenty-ninth day, Rani was presented with the contents of two royal storehouses. On the thirtieth and final day, two hundred and fifty-six elephants crossed the province, carrying the contents of the last four royal storehouses-- Five hundred and thirty-six million, eight hundred and seventy thousand, nine hundred and twelve grains of rice. Altogether, Rani had received more than one billion grains of rice. The raja had no more rice to give. "And what will you do with this rice," said the raja with a sigh, "now that I have none?" "I shall give it to all the hungry people," said Rani, "and I shall leave a basket of rice for you, too, if you promise from now on to take only as much rice as you need." "I promise," said the raja. And for the rest of his days, the raja was truly wise and fair, as a raja should be