Jaya Legge

2021-02-06

The exponential models the population of the indicated country, A, in millions, t years after 20006. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?

Country 1:$A=26.3{e}^{0.029t}$

Country 2:$A=127.7{e}^{0.007t}$

Country 3:$A=148.5{e}^{-0.0091t}$

Country 4:$A=1094.2{e}^{0.016t}$

Country 1:

Country 2:

Country 3:

Country 4:

Caren

Skilled2021-02-07Added 96 answers

Given:

The exponential model that describe the population of different countries:

Country 1:

Country 2:

Country 3:

Country 4:

Population growth is equal to differentiation of exponential model with respect to ‘t’,

So now differentiating the given function one by one:

To check which one is larger, by comparing the quantities of growth rate it can be concluded that:

Country 4:

Has the greates growth rate.

To find the percentage change in population:

Country 4:

Now put

Now put

Now,

Percentage change

Percentage change

Answer: The final answer is given below:

Country 4:

Has the greates growth rate.

Percentage change in population each year

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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