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

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jolis1796 jolis1796 · Answer 1 · 2020-04-18T09:02:56+02:00

Answer:

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.