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There are 225 wolves in a state park. The population is increasing at the rate of 15% per year. When will the population reach 500?

1 Answer

Apr 16, 2016

Between years 5 and 6.

Explanation:

Population after $n$ $n$ years is given by the formula
$XXX P_{n} = 225 \times {(1.15)}^{n}$ $color(white)("XXX")P_n=225xx(1.15)^n$

We are asked when
$XXX P n = 500$ $color(white)("XXX")Pn = 500$

$XXX 225 \times {(1.15)}^{n} = 500$ $color(white)("XXX")225xx(1.15)^n = 500$

$XXX \to {1.15}^{n} = \frac{500}{225} = \frac{20}{9}$ $color(white)("XXX")rarr 1.15^n = 500/225=20/9$

$XXX {log}_{1.15} (\frac{20}{9}) = n$ $color(white)("XXX")log_(1.15) (20/9) = n$

Using a calculator
$XXX {log}_{1.15} (\frac{20}{9}) \approx 5.7133$ $color(white)("XXX")log_1.15 (20/9) ~~5.7133$

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