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 exponen model, A(t) = Aoekt. %3D India: A(t) = 1173.1e0.0008t Iraq: A(t) = 31.5e0.019t Japan: A(t) = 127.3e-0.006t Russia:A(t) = 141.9e¬0.005t %3D %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.

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. Year

Due 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?

U.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 dollars