Question

The table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025.

Country20152025Country A8.98.1Country B32.434.9Country C1367.51406.9Country D61.165.0Country E328.9351.8

(a) Find the exponential growth or decay model 

y = ae^bt or y = ae^−bt

 for the population of each country by letting 

t = 15

 correspond to 2015. Use the model to predict the population of each country in 2035. (Round your values of b to five decimal places. Round your values of a to one decimal place. Round your population predictions for 2035 to one decimal place.) 

CountryExponential ModelPopulation in 2035 
(in millions)Ay = 

 

 By = 

 

 Cy = 

 

 Dy = 

 

 Ey = 

 

 

(b) You can see that the populations of Country D and Country E are growing at different rates. What constant in the equation 

y = ae^bt

 gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.

The constant b determines the growth rate. The greater the rate of growth, the smaller the value of b.The constant a determines the growth rate. The greater the rate of growth, the greater the value of a.    The constant b determines the growth rate. The greater the rate of growth, the greater the value of b.The constant a determines the growth rate. The greater the rate of growth, the smaller the value of a.

Answer 1