5. A rancher is selling off 7% of her ranch each year. If she owns 2000 square miles, in about how many years will she own only 600 square miles? If she starts with 100% of the land and sells 7%, she will have 93% of the land left. After n years, she will have 2000(0.93)" of the land left. 2000(0.93)" 600 = 0.93" 0.3 = log0.3 = log0.93" = n log0.93 log 0.3 log 0.3 log 0.93 0.3 log 0.93 -0.49 = n A negative value does not make sense. The rancher will never have only 600 square miles of land.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
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5. A rancher is selling off 7% of her ranch each year. If she owns 2000 square miles, in
about how
many years will she own only 600 square miles?
If she starts with 100% of the land and sells 7%, she will have 93% of the land left. After n
years, she will have 2000(0.93)" of the land left.
2000(0.93)"
600 =
0.93"
0.3 =
log0.3 = log0.93"
= n log0.93
log 0.3
log 0.3
log 0.93
0.3
log
0.93
-0.49 = n
A negative value does not make sense. The rancher will never have only 600 square miles
of land.
Transcribed Image Text:5. A rancher is selling off 7% of her ranch each year. If she owns 2000 square miles, in about how many years will she own only 600 square miles? If she starts with 100% of the land and sells 7%, she will have 93% of the land left. After n years, she will have 2000(0.93)" of the land left. 2000(0.93)" 600 = 0.93" 0.3 = log0.3 = log0.93" = n log0.93 log 0.3 log 0.3 log 0.93 0.3 log 0.93 -0.49 = n A negative value does not make sense. The rancher will never have only 600 square miles of land.
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