Step 1 :The exponential models given in the question are of the form \(A = P e^{rt}\), where \(P\) is the initial population, \(r\) is the rate of growth or decay, and \(t\) is the time in years. If \(r\) is positive, the population is increasing; if \(r\) is negative, the population is decreasing. The rate of decrease is given by \(-r\) as a percentage. So, we need to identify the countries with negative \(r\) values and calculate the percentage decrease for each.
Step 2 :The rates for each country are as follows: Country B: 0.006, Country C: 0.015, Country D: -0.0051, Country E: -0.002.
Step 3 :The countries with decreasing populations are those with negative rates. These are Country D and Country E.
Step 4 :The rate of decrease for each country is given by \(-r\) as a percentage. Therefore, the population of Country D is decreasing by 0.51% each year and the population of Country E is decreasing by 0.2% each year.
Step 5 :Final Answer: The correct choice is C. Country D and Country E have the decreasing populations. The population of Country D is decreasing by \(\boxed{0.51\%}\) each year and the population of Country E is decreasing by \(\boxed{0.2\%}\) each year.