 # The exponential models describe the population of the indicated country, A, in millions, t years after 2010.Which country has the greatest growth rate? By what Wribreeminsl 2020-11-03 Answered

The exponential models describe the population of the indicated country, A, in millions, t years after 2010.Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
India, $A=1173.1{e}^{0.008t}$
Iraq, $A=31.5{e}^{0.019t}$
Japan, $A=127.3{e}^{0.006t}$
Russia, $A=141.9{e}^{0.005t}$

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The exponential model that describes the population of the indicated country A, in millions,t years after 2010 is
India, $A=1173.1{e}^{0.008t}$
Iraq, $A=31.5{e}^{0.019t}$
Japan, $A=127.3{e}^{0.006t}$
Russia, $A=141.9{e}^{0.005t}$
Here value of k represents the growth rate of population.
Comparing the exponential model from
Standard equation $A={A}_{0}{e}^{kt}$,
value of k for country
India is 0.008, for
Iraq is 0.019, for
Japan is −0.006 and for
Russia is -0.005
Since country Russia and Japan has negative value of k,
Rightarrow the decay rate or population is decreasing as the time increases.
Now arrange the positive value of in descending order:
Since the country Iraq has greatest value of k, so the country Iraqgreatest growth rate. The
growth rate of population of Iraq each year is
$0.019\cdot 100=1.9\mathrm{%}$