Dan and Alan take turns mowing the grass of a yard that is 2400 square yards in area. Dan takes an hour to mow the whole lawn us
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Since represents the number of years passed since 2005, in 2005 we have
, and in 2015 we have
. Let
represent the profits of Jones and Davis, respectively, at year y.
We have
Choosing the best company somehow depends on how much time you can wait: Jones start with a higher value (10 vs 8), but it has a descending trend, because the multiplicative factor goes to zero as t grows.
On the other hand, Davis starts with a smaller value, but tends to infinity as t grows.
So, if you need an immediate result, the most valuable company is Jones, otherwise you're certain can Davis will eventually become bigger.
More precisely, we have
So, after 11 years, Davis will overcome Jones.