Ch 10 Notes Part 2 of 2

# Ch 10 Notes Part 2 of 2 - Your boss has given you the...

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Your boss has given you the following two options for how he will pay you over the next 30 days. Option 1: \$1000 for each day of work Option 2: One cent for the first day, 2 cents for the second day, 4 cents for the third day, 8 cents for the fourth day, and so on Which option will you choose?

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Option 1 30(1000) = 30,000 Option 2 .32 6 .16 5 .08 4 .04 3 .02 2 .01 1 Amount Day Move over Donald Trump! Not too bad for only 30 days! You’ve made a whopping \$0.63 for 6 days of work!
5.12 10 2.56 9 1.28 8 .64 7 .32 6 .16 5 .08 4 .04 3 .02 2 .01 1 Amount Day 5,242.88 20 2,621.44 19 1,310.72 18 655.36 17 327.68 16 163.84 15 81.92 14 40.96 13 20.48 12 10.24 11 Amount Day 5,368,709.12 30 2,684,354.56 29 1,342,177.28 28 671,088.64 27 335,544.32 26 167,772.16 25 83,886.08 24 41,943.04 23 20,971.52 22 10,485.76 21 Amount Day You’re still only making \$10.23 for 10 days of work! Option 2 Now things are starting to look interesting. You’ll be making \$5,242.88 just for one day!!!

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You would make \$5,368,709.12 for working on the 30 th day. Adding up all 30 days of work would mean you would have made a grand total of \$10,737,418.23
.01 Calculations 6 5 4 3 2 1 Amount Day Amount you would make on the Nth day Notice that the exponent is always one less than the day Is there a formula for this? = 0.01·2 (N – 1) (.01)·2 (.01·2)2 (.01·2·2)2 (.01·2·2·2)2 (.01·2·2·2·2)2 .01·2 .01·2 3 .01·2 4 .01·2 5 .01·2 1 .01·2 0 2 That’s a lot of 2s. Is there are better way to write this?

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Amount on the Nth day = 0.01·2 (N – 1) How much would you make on the 40 th day?
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## This note was uploaded on 05/06/2008 for the course MATH 110 taught by Professor Pietro during the Spring '08 term at SUNY Fredonia.

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Ch 10 Notes Part 2 of 2 - Your boss has given you the...

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