The population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.
The final value of any quantity growing constantly at a particular rate is given as [tex]V = V_{0}e^{rt}[/tex] ,
where V is the final value, V₀ is the initial value, r is the rate of growth per time period, and t is the number of time periods.
The current population of squirrels (V₀) = 100.
The growth rate (r) = 5% per month.
The time period (t) = 1 year = 12 months.
Hence, the final population of squirrels (V), is given as:
[tex]V = V_{0}e^{rt}[/tex] ,
or, [tex]V = 100e^{(0.05*12)}[/tex] ,
or, [tex]V = 100e^{0.60}[/tex] ,
or, V = 100*1.822119,
or, V = 182.2119 ≈ 182.
Therefore, the population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.
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