Chapter 3, Section 3.2, Question 044 In 2009, the population of Hungary1 was app

Question

Chapter 3, Section 3.2, Question 044 In 2009, the population of Hungary1 was approximated by P = 9.906(0.997)! where P is in millions and t is in years since 2009. Assume the trend continues. (a) What does this model predict for the population of Hungary in the year 2019? Round your answer to two decimal places. This model predicts the population in the year 2019 is (b) How fast (in people/year) does this model predict Hungary's population will be decreasing in the year 2019? Give your answer to the nearest thousand. million. This model predicts that in 2019, Hungary's population will be decreasing by -https://www.cia.gov/library/publications/the-world-factbook/print/hu.html, accessed April 14, 2009. Click if you would like to Show Work for this question: Open Show Work people per year

Explanation / Answer

P =9.906 * (0.997)^t

t = 0 means 2009

In 2019, it will be t = 10

So, 9.906(0.997)^10

9.6128000024559701

As in 9.61 million ----> ANS

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b)
Deriving :

P'= 9.906 * (0.997)^t * ln(0.997)

Plug in t = 10 :

9.906 * (0.997)^10 * ln(0.997)

-0.02888174431770653735563369126 millions per year

29000 ---> ANS

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