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)

Question

Mathematics

Oswaldo Fitzpatrick

1 August, 19:26

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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Answers (1)

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Cassidy Norman · Answer 1

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.