Solve.
-The rabbit population in a forest area grows at the rate of $6 \%$ monthly. If there are 280 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 280 ( 2.7 ) ^ { 0.06 t }$.
A) 559 rabbits
B) 585 rabbits
C) 544 rabbits
D) 572 rabbits

Question

Quizplus · Accepted Answer

The given formula for the rabbit population growth is $y = 280(2.7)^{0.06t}$, where $t$ is the time in months. To find the population by next September, $t = 12$ months. Substituting $t = 12$ into the formula gives $y = 280(2.7)^{0.06 \times 12}$. Simplifying inside the exponent first: $0.06 \times 12 = 0.72$, so the equation becomes $y = 280(2.7)^{0.72}$. Calculating $2.7^{0.72}$ and then multiplying by 280 gives the expected number of rabbits. The calculation yields a value close to the option D, 572 rabbits, when rounded to the nearest whole number.

Solve -The Rabbit Population in a Forest Area Grows at the Rate

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-The Rabbit Population in a Forest Area Grows at the Rate