The population of City Z was 50,000 in 1983 . From 1983 to 2013, the population of City Z doubled every 5 years. Which of the following best models P, the population of City Z from 1983 to 2013,t years after 1983 ? Choose 1 answer: (A) P=50,000(2)^((t)/(5)) (B) P=50,000(2)^(Bx) (C) P=10,000 t+50,000 (D) P=20,000 t+50,000

Question

The population of City Z was 50,000 in 1983 . From 1983 to 2013, the population of City Z doubled every 5 years. Which of the following best models  P, the population of City Z from 1983 to  2013,t years after 1983 ? Choose 1 answer: (A)  P=50,000(2)^((t)/(5)) (B)  P=50,000(2)^(Bx) (C)  P=10,000 t+50,000 (D)  P=20,000 t+50,000

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Understand the problem: Understand the problem. We need to find a formula that models the population growth of City Z from 1983 to 2013, where the population doubles every 5 years.Analyze answer choices: Analyze the given answer choices. We are given four different formulas and we need to choose the one that correctly models the population growth.Determine correct model: Determine the characteristics of the correct model. Since the population doubles every 5 years, we are looking for an exponential growth model. The base of the exponent should be 2, and the exponent should represent the number of 5-year periods that have passed since 1983.Eliminate incorrect choices: Eliminate incorrect answer choices. Option (C) P=10,000 t+50,000 and option (D) P=20,000 t+50,000 are linear models, which do not represent exponential growth. Therefore, they can be eliminated.Compare exponential models: Compare the remaining exponential models. Option (A) P=50,000(2)^((t)/(5)) and option (B) P=50,000(2)^(Bx) are left. Option (B) is incorrect because it includes an undefined variable Bx, which does not relate to the problem statement. Therefore, option (B) can be eliminated.Verify correct model: Verify the correct model. Option (A) P=50,000(2)^((t)/(5)) correctly represents the population doubling every 5 years. To verify, if t=5 (which is 5 years after 1983), the population should be 50,000 * 2 = 100,000. Let's check: P = 50,000(2)^((5)/(5)) = 50,000(2)^1 = 50,000 * 2 = 100,000. This matches the doubling pattern described in the problem.

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