A local government agency has asked you to consult regarding acquisition of land
ID: 1812618 • Letter: A
Question
A local government agency has asked you to consult regarding acquisition of land for recreation needs for the urban area. The following data are provided:
Urban population 10 years ago 49,050
Urban area population now 89,920
Desired ratio of recreation land in
acres per 1,000 population 10 acres/1,000
Actual acres of land now held by local
government for recreational purposes 803 acres
a. Find the annual growth rate in the urban area by assuming that the population grew at a compounded annual rate over the past 10 years.
b. How many years ago was the desired ration of recreation land per 1,000 population exceeded if no more land was acquired and the population continued to grow at the indicated rate?
c. The local government is planning to purchase more land to supply the recreational needs for 10 years past the point in time found in part (b). How many acres of land should they purchase to maintain the desired ratio, assuming that the population growth continues at the same rate?
Explanation / Answer
a) Annual growth rate= (89,920/49,050)1/10-1
= 1.0625 -1
= 0.0625 or 6.25%
b) 49.05/80.3 = 0.61080.6108*(1.0625)
= 0.64900.6490*(1.0625)
= 0.68960.6896*(1.0625)
= 0.73270.7327*(1.0625)
= 0.77850.7785*(1.0625)
= 0.82710.8271*(1.0625)
= 0.87880.8788*(1.0625)
= 0.93370.9337*(1.0625)
= 0.99210.9921*(1.0625)
= 1.054
In 9th year desired ratio of recreation land per 1,000 population exceeded.Therefore, its 1 year ago.
c) 1.054 = 49.05/ landLand
= 46.54 acres
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