Chapter 10.1, Problem 32E

Land Use In one state, a Board of Realtors land use survey showed that 35% of all land was used for agricultural purposes, while 10% was urban. Ten years later, of the agricultural land, 15% had become urbanized and 80% had remained agricultural. (The remainder lay idle) Of the idle land, 20)% had become urbanized and 10% had been converted for agricultural use. Of the urban land. 90% remained urban and 10% was idle. Assume that these trends continue,

(a) Write a transition matrix using this information.

(b) Write a probability vector for the initial distribution of land.

Find the land use pattern after the following time periods.

(c) 10 years (d) 20 years

(e)Write the transition matrix, for a 20-year period.

(f) Use your result from part (e) to find the probability that an idle plot of land is still idle 20 years later.