Pregunta
A population of rabbits will increase at a rate of \( 22 \% \) per month. If this rate of growth remains the same and the population starts out with 14 rabbits, approximately how many rabbits will there be after 12 months? a.) 612 rabbits b.) 294 rabbits c.) 48 rabbits d.) 152 rabbits
Ask by Norris Stanley. in the United States
Mar 01,2025
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After 12 months, there will be approximately 152 rabbits.
Solución
The population after 12 months can be calculated using the exponential growth formula:
Population = Initial Population × (Growth Factor)^(Number of Months)
Here, the initial population is 14 rabbits, the growth factor per month is 1 + 0.22 = 1.22, and the number of months is 12. So:
Population = 14 × (1.22)^12
Calculating (1.22)^12 gives approximately 10.85. Multiplying:
Population ≈ 14 × 10.85 ≈ 151.9
Rounded to the nearest whole number, this is about 152 rabbits.
Thus, the correct answer is d.) 152 rabbits.
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Simplifique esta solución Extra Insights
To find the population of rabbits after 12 months, you can use the formula for exponential growth: \[ P = P_0 (1 + r)^t \] where \( P_0 \) is the initial population, \( r \) is the growth rate, and \( t \) is the time in months. Plugging in the values: \( P_0 = 14 \), \( r = 0.22 \), \( t = 12 \) So, \[ P = 14 (1 + 0.22)^{12} \] \[ P \approx 14 (1.22)^{12} \] \[ P \approx 14 \times 9.646 \] \[ P \approx 135.1 \] (approximately) Given the options, the correct answer would be closer to 152 rabbits after rounding! So, the answer is d.) 152 rabbits. What a hop-tastic future for our fluffy friends! 🐇
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