The exponential models describe the population of the indicated country, A, in millions, t years after 2006. a. Which country has the greatest growth rate? b. By what percentage is the population of that country increasing each year? Country 1 : Upper A equals 145.9 e Superscript negative 0.003 t Country 2 : Upper A equals 1097.7 e Superscript 0.016 t Country 3 : Upper A equals 28.6 e Superscript 0.022 t Country 4 : Upper A equals 130.2 e Superscript 0.005 t

a) Country 3

b) 2.2%

Step-by-step explanation:

Given

Country 1 : A = 145.9*e∧ (-0.003*t)

Country 2 : A = 1097.7*e∧ (0.016*t)

Country 3 : A = 28.6*e∧ (0.022*t)

Country 4 : A = 130.2*e∧ (0.005*t)

a) Country 3 has the highest growth rate, as it has the largest exponent in its growth function.

b) A (t+1) / A (t) is the ratio of one year's population to the previous year's. For Country 3, this is

A (t+1) / A (t) = 28.6*e∧ (0.022 * (t+1)) / 28.6*e∧ (0.022*t) = e∧ (0.022) = 1.022 to 3 decimal places.

Thus, Country 3's population is increasing by 2.2% each year.