Question

A population of squirrels is growing in a Louisiana forest with a monthly growth constant of 55 percent. If the initial count is 100100 squirrels, how many are there in a year? Round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to the nearest whole number.

Answer 1

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 $V = V_{0}e^{rt}$ ,

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:

$V = V_{0}e^{rt}$ ,

or, $V = 100e^{(0.05*12)}$ ,

or, $V = 100e^{0.60}$ ,

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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