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Ce Ca me | myLU HW: 4.8 and 5.6 Assignment x PNR Co oc oe Ra eRe et ORME NS ae TS SC LC url ea Ca aa taco Cad Cas Coleen ne Re AU Re een cca read a) 'Anew resort opens in Costa Rica that is managed by a retired math professor with a strange sense of humor. Patrons can choose one of three payment options. In each case, the cost decreases each day, and you have to leave when it reaches zero. Option 1: Per-person cost is $240 the first day, then decreases by $30 every day. Option 2: Per-person cost is $600 the first day, $300 the second day, and in general, every day is half as much as the previous day. Option 3: Per- person cost is $400 the first day, and in each successive day, you subtract 10 times the square of the number of days you've been there from the previous day's cost. oo Part 1 of 3 (a) Which option is the best if your primary goal is to spend the least amount of money? How much would you spend, and for how many days? If your goal is to spend the least amount of money then the cheapest option is Option | \\ . You would spend $| 1080 | and stay | 8 | days. 0 @ Part 2 of 3 (b) Which option is best if your primary goal is to stay the longest? If your goal is to stay the longest you should choose Option Pat: 2/3 Part 3 of 3 (c) Which type of decline is illustrated by each option? Option | illustrates Select v ) decline. Option 2 illustrates| select | decline. Option 3 illustrates | Select v | decline. (Skip Part ) (Save For Later) (~ ey S 7 $+{T==~ ) ( Submit Assi it (Submit Assignment ) eo aC en ek mmc nd Enea) Pe isco boum Q. AlChat with PDF Upload for Unlocks ExpertHelp Study Resources ~ + Option 1 (arithmetic decrease): daily cost an = 240 30(n 1). + Reaches zero when 240 30(n 1) = 0 n = 9. So you pay for days 1-8. + Sum for 8 days: 8 S= pla + an) = 5 (240 + 30) = 4- 270 = 1080. + Option 2 (halving each day): costs 600, 300, 150, .... Total if continued indefinitely is a geometric sum 600/(1 1/2) = 1200, which is more than 1080. + Option 3 (subtracting a quadratic amount each day) drops quickly but the partial sums before cost hits zero or below are at least 1140 (depending on interpretation), still more than 1080. Thus, to minimize total spending, pick Option 1: spend $1080 over 8 days. Verify with tutor solve this problem Answer explanation Option 2. Explanation: + Option 1: 240, 210, 180, ... decreases by 30 each day. It hits 0 after 8 days (must leave), so you can stay 8 days. + Option 3: 400, then subtract 10(n 1)? each day: 400, 390, 350, 260, 100, then it would go below 0 on day 6, so you can stay 5 days. + Option 2: halves each day (600, 300, 150, forced to leave. .). This sequence never reaches 0, so you are never Therefore. to stav the lonaest. choose Option 2. @ Attach image Upload doc