A state park had a population of 330 rabbits. The population grew, with continuous compounding at a rate of 15% per year for 12years. How many rabbits were in the park after the 12 years?

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christopherturn1 christopherturn1 · Answer 1 · 2019-05-06T06:23:17+02:00

330(1.15)^12=1765.58

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shrutiagrawal1798 shrutiagrawal1798 · Answer 2 · 2021-11-30T19:03:59+01:00

The population of rabbits grew continuous compounding so formula for continuously compounded will apply.

The rabbits were in the park after 12 years is 1,996 rabbits.

Given:

The population of rabbit is [tex]P=330[/tex].

The rabbit increasing rate is [tex]r=15\%[/tex].

Time is [tex]t=12\:\rm year[/tex].

Apply the formula for continuously compounded to calculate the number of rabbit after 12 year.

[tex]A=Pe^{rt}[/tex]

Substitute the value.

[tex]A=330.00(2.71828)^{(0.15)(12)}\\A=1,996.38 \\A\approx1996[/tex]

Thus, the rabbits were in the park after 12 years is 1,996 rabbits.

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