Question

Chapter 10.1, Problem 9E 2 Bookmarks Show all steps: ON < Exercise deal with data from the U.S. Bureau of the Census on populations of major cities These data allow us to find how fast the population is growing and when it will reach certain levels. Such calculations are very important, because they indicate the future needs of the population for goods and services and how well the area can support the population a. Develop the model that represents the population of Chicago (see Exercise). b. Predict the population in 2019. c. Predict the population in 2024. d. Predict when the population will be double its 2011 population Exercise The third largest city in the United States is Chicago. Its population in 2011 was 2,705 (in thousands); in 2012, it was 2,715. a. Convert this information to two ordered pairs (pl. where I measures years since 2011 and p measures population in thousands. b. Find Al, the change in time c. Find Ap, the change in population. d. Find Ap/At, the average growth rate. e. Find (Aplanip, the relative growth rate. Chicago is the third largest city in the United States 4o * ? A.

Answer 1

Solution:

Exercise, Solution : O] To convert: given in formation in two ordered pairs So. (top): 0011, 2705) and a 1 (t.2, P2) = (2012, 2715) b] At - t2-t, - 2012 - 2013 od Thus. Atas c) To find: AP op - Pa-p, - 2715 - 2705 = 10 d] to find : AP At los by using value of op and ot obtained in cc) de parts respectively LO be = 10 ej to find: de en (relative growth rate) Substitute P= Pp and value of AP obtained in a gives, - it un teh otobugt = 2705 To 2705

a] to develop We have slope D = develop : model which represents population of Chicago. ve Slope AP - 10 and a point (2011, 2705) use the formula of line equation is - y-y = mc2-x) mis Slope that is growth rate bere , malo " CX, 34,) = (tis P.) = (2011, 2705) oy. Substiterting values in formula, it gives Where, mis slope p -2705 = 10(-2011) 5p -2705= 103-20110 >p = 107-20110 + 2705 Ps 103-17405 b] to find : population in 2019 Substitute t=2019 in Polot -17405 = P = 10x 2019 -17405 - 20190-17405 = 2785 Hence, population in 2019 is 2785 Cin thousands) c) to find i population in 2024 Substitute t= 2024 in Ps 107-17405 7 Ps 10x2024-17405 20240-17405 - 2835

d] To find: When the population of 2011 doubles. so here P=2(2705) = 5410 plug, p=5410 in p= lot-17405 5410 = 10t-17405 → Tot - 5410+ 17405 * 10t= 22815 » I = 22815 - 228115 2282 T So, In 2282 population doubles.