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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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
Transcribed Image Text:12. The following exponential models describes the population (in million of people) of the indicated
country starting at 2010. (Let t=0 correspond to the year 2010). All of the equations use the exponential
model, A(t) = Aoekt.
%3D
India: A(t) = 1173.1e0.0008t
Iraq: A(t) = 31.5e0.019t
Japan: A(t) = 127.3e-0.006t
%3D
%3D
Russia:A(t) = 141.9e¬0.005t
%3D
Based on the exponential models for each country, answer the following questions:
(a) What was the population (in millions of people) of Japan in 2010?
(b) Which country has the greatest growth rate? What is the growth rate? (State as a percentage.)
(c) Using the exponential model for Japan's population, in what year will Japan's population drop to
100 million people? Show all necessary algebraic work. Round to the nearest year.
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- According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model t – 2008 P(t) = 304 · (1.011)* represents the population P (in millions of people) in year t. According to the model, when will the population be 366 million people? Be sure to round your answer to the nearest whole year. Yeararrow_forwardDue to the rising temperatures in a bay ecosystem, the population mass of a certain species of jellyfish is growing exponentially. When first measured in 2010 (which we can call year t = 0), the bay contained about 600 tons of jellyfish. Now in 2021 (t = 11), the bay has 2,000 tons. If it continues to grow in this way, in what year will the jellyfish population mass reach 10,000 tons?arrow_forwardU.S. health-care expenditures have been growing exponentially during the past two decades. In 2008, expenditures were 2.4 trillion dollars with a growth rate of 9%. Lawmakers hope to decrease the annual growth rate to 2%. Compare the two rates graphically and algebraically as follows. (a) For each growth rate, find an exponential model for the health-care expenditures t years since 2008. f9%(t) = f2%(t) = (c) Find the predicted health-care expenditures in 2020 for each model. (Round your answer to two decimal places.) f9%(12) = trillion dollars f2%(12) = trillion dollarsarrow_forward
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