The population of a town was 230000. For 12 years, the population grew 4% per year, compounded continuously. When was the popula
tion at the end of the 12 year period according to the exponential growth function?
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Let . Then
for all
, so
is strictly increasing. As
,
, so
is bounded above by 1. This is to say,
and the integral of converges over the same domain, so this integral must also converge by comparison.
We have, by setting ,