Solve the problem. Round to the nearest cent as needed.
-The rabbit population in a forest area grows at the rate of 6% monthly. If there are 230 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. Use e
A) 447
B) 457
C) 483
D) 470

Question

Solve the problem. Round to the nearest cent as needed.
-The rabbit population in a forest area grows at the rate of 6% monthly. If there are 230 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. Use e 
A) 447 
B) 457 
C) 483 
D) 470

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for exponential growth:

A = P(1 + r)n

where: 
A = final amount (number of rabbits)
P = initial amount (number of rabbits in April)
r = growth rate per period (6% per month, or 0.06)
n = number of periods (12 months)

Plugging in the values we know, we get:

A = 230(1 + 0.06)12 
A = 230(1.06)12 
A ≈ 469.95

Rounding to the nearest whole number, we get:

A ≈ 470

Therefore, the expected number of rabbits by next April is approximately 470. The closest choice to this value is D, 470. To solve the problem, we can use the formula:

P = P0 (1 + r)^n

where: 
P0 = initial population (given as 230 rabbits)
r = monthly growth rate (6% = 0.06)
n = number of months (12, since we want to know the population after one year)

Substituting these values:

P = 230 (1 + 0.06)^12 
P ≈ 469.69

Rounding to the nearest whole number: 
P ≈ 470

Therefore, the expected number of rabbits (rounded to the nearest whole number) by next April is 470.

The closest choice is D (470), so it is the best choice.

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