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The population (in millions) of a certain country t years after 1900 is given by the function p(t). There were 480 million in 1900. If p′(t)=3 throughout the time span 1900 to 1910, what was the population of the country in 1907? (Hint: What was the practical signifigance of p′(t)=3 )

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mauricioalessandrell

Answer:

The population of the country in 1907 was 501 million.

Step-by-step explanation:

Hi there!

The population is given by the function p(t)

We know that p(0) = 480 million and that p´(t) = 3.

p´(t) is the derivative of the function p(t) and expresses the variation (or rate of change) of the population with respect to "t". In this case, p´(t) = 3 indicates that the population increases by 3 million per year (because t is in years) from 1900 to 1910. Then, in 1907 the population will be:

480 million + 3 million / year · 7 year = 501 million.

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