Complete the table shown to the right for the population gro

Complete the table shown to the right for the population growth model for a certain country. k = (Round to four decimal places as needed.)

Solution

The population growth function is y = y₀ e^kt here, y₀ is the initial population in 2004 which is 19.6 million and y is the projected population in 2027 which is 37.1 million. Also t = 2027 – 2004 = 23 years. Therefore, 37.1 = 19.6e^23k or, e^23k = 37.1/19.6. On taking natural logarithm of both the sides, we have ln(37.1) – ln(19.6) = 23k ln (e) = 23k [ as ln (a/b) = ln (a) – ln( b) and ln (e) = 1] or, 23k = 3.61361697 – 2.975529566 = 0.638087403. Therefore, k = 0.638087403/23 = 0.02774293 = 0.0277 ( on rounding off to 4 decimal places)