Final answer:
The predicted population of a country with an initial population of 300 million in 2006 and a growth rate of 1.4% is approximately 744.48 million in the year 2071, calculated using the exponential growth formula.
Step-by-step explanation:
Using a growth rate of 1.4% to predict the population in 2071 from a 2006 baseline requires the use of the exponential growth formula. Given a starting population of 300 million, we can use the formula P = P0 * (1 + r)^t, where P is the final population, P0 is the initial population, r is the growth rate (expressed as a decimal), and t is time in years. The formula derives from the general compound interest formula, which also applies to population growth. In this case, P0 is 300 million, r is 0.014 (after converting 1.4% into decimal form), and t is the number of years from 2006 to 2071, which is 65 years. Plugging the values into the formula, we get P = 300 million * (1 + 0.014)^65.
To calculate this without a calculator, we can use the rule of 70, which indicates that a population will approximately double every 70/r years, where r is the growth rate in percent. Since 1.4% would result in a doubling time of about 50 years (70/1.4), we would expect the population to double more than once from 2006 to 2071. Thus, the 2071 population would be greater than 600 million but less than 1200 million. However, to get a precise figure, calculating P yields a population of approximately 300 million * (1 + 0.014)^65 ≈ 300 million * 2.4816 = 744.48 million. Therefore, the predicted population of the country in 2071 is approximately 744.48 million people.