University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2014
Views:

21

Pages:

2
Author:

Raelynn Roy

10.2 LINEAR GROWTH MODEL WORKSHEET SOLUTIONS For each of the following linear growth model, • Find an explicit description and the 9th generation of the population, P9 1) P0 = 718 and d = 32 5) P5 = 71 and P6 = 84 PN = 718 + 32N d = 84 – 71 = 13; P0 = 71 – 13(5) = 6 P9 = 718 + 32(9) = 1006 PN = 6+ 13N P9 = 6 + 13(9) = 123 2) 2, 19, 36, 53, … d = 17 = 19 – 2 6) P13 = 96 and P14 = 105 d = 105 – 96 = 9; P0 = 96 – 9(13) = -21 PN = 2 + 17N P9 = 2 + 17 (9) = 155 PN = -21 + 9N P9 = -21+ 9(9) = 60 3) 1123, 1332, 1541, 1750, … d = 209 = 1332 – 1123 7) P6 = 65 and P15 = 128 PN = 1123 + 209N d = (128 – 65)/(15-6) = 7; P0 = 65 – 7(6) = 23 P9 = 1123 + 209(9) = 3004 PN = 23 + 7N 4) 9.6, 10.05, 10.5, 10.95, … P9 = 23 + 7(9) = 86 d = 0.45 = 10.05 – 9.6 8) P21 = 2170 and P90 =5896 PN = 9.6 + .45N d = (5896 – 2170)/(90-21) = 54; P9 = 9.6 + .45(9) = 13.65 P0 = 2170 – 54(21) = 1036 PN = 1036 + 54N P9 = 1036 + 54(9) = 1522 9) Every 3 months, Marcus buys himself 4 new neckties. Let P0 represent the number of neckties he starts with and PN be the number of neckties in his collection at the end of Nth 3-month period. Assume that he started out with 3 neckties and he never throws away one. a. What is the population in this problem? Neckties b. What is the transition? 3 – months c. What is the transition rule? PN = PN-1 + 4; Adding 4 neckties 10) A population of lab rats is going to be increased by 3 rats a month. If it costs $3.50 to care for each rat a month and there were 2 rats to begin with in the lab, then how much will the lab be paying for the rats after 10 months? Assume all rats survive lab work. P10 = 2 + 3(10) = 32 rats; 32(3.50) = $112 For each of the following linear growth model, find the given sum 11) 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26 + 29 15) P0 = 111 and d = 31; = (5 + 29)*9/2 = 153 P0 + P1 + … + P254 P254 = 111 + 31(254) =7985 (111 + 7985)*255/2 = 1,032,240 12) P0 = 115 and P29 = 318; P0 + P1 + P2 + … + P29 16) P0 = 12 and d = 4.5; = (115 + 318)*30/2 = 6495 P50 + P51 + … + P119 13) For 50 terms, 29 + 44 +59 +… P50 = 12 + 4.5(50) = 237 P119 = 12 + 4.5(119) = 547.5 P49 = 29 + 15(49) = 764 (237 + 547.5)*70/2 = 27,457.5 = (29 + 764)*50/2 = 19,825 14) For 125 terms, 421 + 427 + 433 + … P124 = 421 + 6(124) =1165 (421 + 1165)*125/2 = 99,125 17) 5 + 17 + 29 + 41 + … + 1157 1157 = 5 + 12N; N = 96 (5 + 1157)*97/2 = 56,357 18) 9012 + 8895 + 8778 + … + 7140 7140 = 9012 – 117N; N = 16 (9012 + 7140)*17/ 2 = 137,292 19) A small business sells $6,500 worth of products during its first year of business. The owner has set an annual goal for increased sales at $3500 for 15 years. Find the total sales during the first 8 years this business is in operation. N = 0  First Year, N = 7  8th year P7 = 6500 + 3500(7) = 31,000 (6500 + 31,00)*8/2 = $150,000 20) Cosmic Java opened in 2005 with 21 coffee shops and plans to open 13 new coffee shops each year after that. Suppose it costs the company $45,000 each year to maintain one coffee shop. a. How many Cosmic Java coffee shops will there be in 2020? N = 0  2005, 2020  N = 15 21 + 13(15) = 216 SHOPS b. In what year will Cosmic Java reach the milestone of having 300 coffee shops? 300 = 21 + 13N; N = 21.5 or between 2026 and 2027 c. In 2010, how much money will the company have used to maintain all its coffee shops since 2005? P5 = 21 + 13(5) = 86; (21 + 86)*6/2 = 321 Shops; 321*45000 = $14,445,000