<p>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) =7 throughout the time span 1900 to 1910, what was the population of the country in 1907? (Hint: What was the practical significance of p’(t)=7 )</p>
<p>The derivative of any function represents the rate of change of the original function, so if p’(t) = 7 throughout 1900-1910, then the population was increasing by 7 million each year. Hope that helps. :-)</p>
<p>So, for each year 7 million increase .Therefore in 7 years (1900 - 1907 = 7 ) increase in population = 7 x 7 = 49 million .
Polulation in 1907 = 480 million + 49 million = 529 million Answer.</p>
<p>well thing of it logically: new amount = old amount + overall change
here, change is represented by integration, so</p>
<p>P(7) = P(0) + integral from 0 to 7 of p’(t) dt = 480 million + integral from 0 to 7 million of 7 dt = 480 million + 49 million = 529 million</p>