MA170wk6solns - MA170 Week 6 Report Ordinary Simple...

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MA170 Week 6 Report: Ordinary Simple Annuities; Arithmetic and Geometric Progressions Name: ______SOLUTIONS______________ Lab: Fall 2010 1. [4 marks ] A lottery gives the jackpot winner the choice of taking one of the following 2 options: (i) $10 000 000 lump sum OR (ii) A payout as follows: $0.01 on the °rst day, $0.02 on the second, $0.04 on the third, and each subsequent day the winner receives twice as much as the day before, continuing for one month (in this case assume the month has 30 days). Taking only the jackpot winnings into account, which option would you rather take? Geometric progressions with n = 30 , t 1 = 0 : 01 , r = 2 S 30 = 0 : 01 + 0 : 02 + 0 : 04 + 0 : 08 + ::: + 0 : 01(2) 29 = 30 X i =1 0 : 01(2) i ° 1 = 0 : 01 ° 2 30 ° 1 2 ° 1 ± = 0 : 01 (1073741823) = $10 ; 737 ; 418 : 23 Thus, I would receive more money by taking the second option, so my choice if I won this lottery would be option (ii) 2. [4 marks ] In the construction of a water well, the cost of drilling the °rst 10 cm into the ground is $6.80. For each additional 10 cm, the cost increases by $2. If the company’s budget allows for $1500 towards the cost of drilling the well, determine how deep a well may be drilled. Express your answer in metres.
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