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According to the Economist the population of Russia has been declining. The population of Russia was 142 million in 2008 and will shrink by 700,000 people in 2009. Write the differential which models change of the Russian population over time. O Pe-0.00493t+1.42 OP=1.42e-0.00439t OP 1.42e-0.7t OP 1.42e0.00493t

According to the Economist the population of Russia has been declining. The population of Russia was 142 million in 2008 and will shrink by 700,000 people in 2009. Write the differential which models change of the Russian population over time. O Pe-0.00493t+1.42 OP=1.42e-0.00439t OP 1.42e-0.7t OP 1.42e0.00493t

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Declining Population Analysis** According to *The Economist*, the population of Russia has been declining. The population of Russia was 142 million in 2008 and will shrink by 700,000 people in 2009. Write the differential which models change of the Russian population over time. 1. \( P = e^{-0.00493t} + 1.42 \) 2. \( P = 1.42e^{-0.00493t} \) 3. \( P = 1.42e^{-0.7t} \) 4. \( P = 1.42e^{0.00493t} \) **Explanation:** The candidate equations describe possible models for the population \( P \) as a function of time \( t \). - The first option suggests an exponential decay with an added constant 1.42. - The second option describes an exponential decay multiplied by 1.42, which seems more practical given the context of population decline. - The third and fourth options involve different exponents and suggest exponential decay and growth, respectively, but at different rates. Understanding these equations helps to identify the model correctly depicting the declining population trend. Examine each differential for its implications on population dynamics over time.
Transcribed Image Text:**Declining Population Analysis** According to *The Economist*, the population of Russia has been declining. The population of Russia was 142 million in 2008 and will shrink by 700,000 people in 2009. Write the differential which models change of the Russian population over time. 1. \( P = e^{-0.00493t} + 1.42 \) 2. \( P = 1.42e^{-0.00493t} \) 3. \( P = 1.42e^{-0.7t} \) 4. \( P = 1.42e^{0.00493t} \) **Explanation:** The candidate equations describe possible models for the population \( P \) as a function of time \( t \). - The first option suggests an exponential decay with an added constant 1.42. - The second option describes an exponential decay multiplied by 1.42, which seems more practical given the context of population decline. - The third and fourth options involve different exponents and suggest exponential decay and growth, respectively, but at different rates. Understanding these equations helps to identify the model correctly depicting the declining population trend. Examine each differential for its implications on population dynamics over time.
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