Question

The exponential models describe the population of the indicated country, A, in millions, tyears after 2006. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year? A = 28.3 0.0231 Country 1: Country 2: Country 3: Country 4: A= 1080.3 e 0.013 A=148.26 -0.0040 A = 132.7 0.0031 Country has the greatest growth rate. The population of that country is increasing by % each year. (Round to the nearest tenth as needed.)

Answer 1

for a exponential function of the form

$\large A=A_0e^{kt}$

growth factor depends on value of k . if k is large posative then growth will be large . then growth percentage is given by

$\large percentage\;of\;growth\;per\;year=(e^{k}-1)*100$

here country 1 has greatest value of k . so

country 1 has the greatest growth rate .

then

$\large percentage\;of\;growth\;per\;year=(e^{0.023}-1)*100=2.3$

so answer is 2.3 %

the population of the country is increasing by 2.3 % per year