The table shows the populations (in millions) of five countries in 2013 and the

Chapter 4, Problem 36

(choose chapter or problem)

The table shows the populations (in millions) of five countries in 2013 and the projected populations (in millions) for 2025. (Source: U.S. Census Bureau)

(a) Find the exponential growth or decay model, \(y=a e^{b t}\) or \(y=a e^{-b t}\), for the population of each country, where t is the year, with t = 13 corresponding to 2013. Use the model to predict the population of each country in 2040.

(b) You can see that the populations of Canada and the Philippines are growing at different rates. What constant in the equation \(y=a e^{b t}\) is determined by these different growth rates? Discuss the relationship between the different growth rates and the magnitude of the constant.

(c) The population of Turkey is increasing while the population of Hungary is decreasing. What constant in the equation \(y=a e^{b t}\) reflects this difference? Explain.

Text Transcription:

y = ae^bt

y = ae^−bt