a population of squirrels is growing in a louisiana forest with a monthly growth constant of 10 percent. if the initial count is 100 squirrels, how many are there in a year? round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to the nearest whole number.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Growth Model", "Continuous Growth Rate" ], "new_concepts": [], "current_concepts": [ "Exponential Growth Model", "Continuous Growth Rate" ] } ## Set up the exponential growth model Using the *Exponential Growth Model* and *Continuous Growth Rate* knowledge points $$ P(t) = P_0 e^{rt} $$ $$ P_0 = 100,\quad r = 0.10 $$ ## Calculate the population after one year Using the *Exponential Growth Model* knowledge point $$ \begin{aligned} t &= 12\ P(12) &= 100 e^{0.10 \times 12}\ &= 100 e^{1.2}\ &\approx 100 \times 3.3201169\ &\approx 332.01169 \end{aligned} $$ ## Round to the nearest whole number Using the *Exponential Growth Model* knowledge point $$ P(12) \approx 332 $$ A population of squirrels is growing in a Louisiana forest with a monthly growth constant of 10 percent. If the initial count is 100 squirrels, how many are there in a year? Round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to the nearest whole number. 332 squirrels { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Exponential Growth Model" ] }

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Explanation:

Set up the exponential growth model

Calculate the population after one year

Round to the nearest whole number

Answer: