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Question 67 – In order to predict the wastewater production, the population number has to be understood. The population data is : 72000 (for year 1961 or P-1961), 85000 (for year 1971 or P-1971), 110500 (for year 1981 or P-1981). (a) Find the average population increase, or [ (P-1981 - P-1971) + (P-1971 - P-1961) ] / 2. (b) Find the average percentage population increase, or [ (P-1981 - P-1971) / P-1971 + (P-1971 - P-1961) / P-1961 ] / (2) X 100. (c) Find the incremental increase or P-1981 - 2 (P-1971) + P-1961. (d) Let Po = P-1981. After 2 decades or n = 2, the population is P-2001. By using arithmetical increase method, find P-2001 = Po + n (Answer for a). (e) By using incremental increase method, find P-2001 = (Answer of d) + n (n + 1) (Answer of c) / 2. (f) By using geometrical increase method, find P-2001 = Po [ 1 + (Answer of b) / 100 ] ^ n where ^ is power sign, or 1 ^ 2 = 1 x 1 = 1. (g) If the actual P-2001 = 184000, which method of estimation is more accurate, based on your answer in (d), (e) and (f)?
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Answer Posted / kang chuen tat (malaysia - pen
Answer 67 – (a) Average population increase = [ (110500 - 85000) + (85000 - 72000) / 2 = 19250. (b) Average percentage population increase = [ (85000 - 72000) / 72000 + (110500 - 85000) / 85000 ] x 100 / 2 = 24.025. (c) Incremental increase = 110500 - 2 (85000) + 72000 = 12500. (d) P-2001 = 2(19250) + 110500 = 149000. (e) P-2001 = 149000 + 2 (3) (12500) / 2 = 186500. (f) P-2001 = 110500 (1 + 0.24025) ^ 2 = 169973. (g) Errors of answers : (d) 184000 - 149000 = 35000, (e) 184000 - 186500 = -2500, (f) 184000 - 169973 = 14027. Answer (e) or incremental increase is more accurate to such data, or the most accurate prediction among the three available formulae. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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