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Solutions for Session 7, Part B
See solutions for Problems: B1 |B2 | B3 | B4 | B5 | B6| B7
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Problem B2 | |
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The total for 25 weeks of plan A, at $2,000 per week, is $50,000. Plan B, which starts at 1 penny and doubles each week totals $335,544.31, including $167,772.16 in the final week.
<< back to Problem B2
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Problem B3 | |
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After 40 weeks, the grand total at this job would be $10,995,116,277.75, including just under $5.5 billion in the last week. Before the end of the year, you would exhaust the total money supply of the United States.
<< back to Problem B3
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Problem B4 | |
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Here is the completed table.
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Years after 1981 | | Estimated Population |
0 | | 350 |
1 | | 399 |
2 | | 455 |
3 | | 519 |
4 | | 591 |
5 | | 674 |
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<< back to Problem B4
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Problem B5 | |
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You can extend the spreadsheet, but an easier way to obtain an answer would be to calculate 350 * (1.14)20 = 4,810 whales. One way to estimate this is to observe that the population seems to be nearly doubling in 5 years (doubling would be 700 whales). This means that we could expect the population to nearly double three more times in a total of 20 years. This doubling would be 350 -> 700 -> 1,400 -> 2,800 -> 5,600, so an estimate is roughly 5,000 whales.
<< back to Problem B5
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Problem B6 | |
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It takes a little more than 5 years. And no, it doesn't matter what the initial population value was, because the ratio of the population after 5 years from now relative to starting population is created only by multiplying 1.14 five times.
<< back to Problem B6
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Problem B7 | |
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One possible pattern is to build, at each stage, a triangle of toothpicks with sides twice as long as the previous triangle.
<< back to Problem B7
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