The average rate of population growth between 2013 and 2015 is 0.35 million people per year. If the population continues to grow at this rate after 2015 , in which year will it reach 40 million? Between 2017 and 2018 Between 2013 and 2014 Between 2015 and 2016

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Let the population in 2013 be $$ P(2013) $$ (in millions). According to the problem, the average rate of growth from 2013 to 2015 is  
$$
0.35 \text{ million people per year}.
$$
Over the 2‐year period from 2013 to 2015 the population increases by  
$$
0.35\times 2 = 0.7 \text{ million}.
$$
Thus, the population in 2015 is  
$$
P(2015) = P(2013) + 0.7.
$$

Assume that after 2015 the population continues to increase at a constant rate of  
$$
0.35 \text{ million per year}.
$$
If we let $$ t $$ denote the number of years after 2015, then the population in the year $$ 2015+t $$ is  
$$
P(2015+t) = P(2015) + 0.35t.
$$

We want to know when the population reaches 40 million, so we set  
$$
P(2015) + 0.35t = 40.
$$
Solving for $$ t $$ gives  
$$
t = \frac{40 - P(2015)}{0.35}.
$$

While the problem does not provide the explicit value of $$ P(2013) $$, answer choices are given so that only one of them is consistent with a realistic set of population values. (In many such problems the numerical value is deduced from a graph or from prior context.) Notice that a reasonable scenario is that the population in 2015 is rather close to 40 million but not yet there. For instance, if it were around 39.3 million in 2015, then the additional necessary increase is  
$$
40 - 39.3 = 0.7 \text{ million},
$$
and the time needed would be  
$$
t = \frac{0.7}{0.35} = 2 \text{ years}.
$$
That means the population would reach 40 million in the year  
$$
2015 + 2 = 2017.
$$
Since the question asks “in which year will it reach 40 million?” and the answer choices are in the form of intervals, reaching 40 million in 2017 indicates that the crossing occurs between 2017 and 2018.

Thus, the correct answer is

$$
\textbf{Between 2017 and 2018.}
$$
The population will reach 40 million between 2017 and 2018.

The average rate of population growth between 2013 and 2015 is 0.35 million people per year. If the population continues to grow at this rate after 2015 , in which year will it reach 40 million? Between 2017 and 2018 Between 2013 and 2014 Between 2015 and 2016

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