A certain developing country has a population of 500,000. The yearly rate of increase of literacy among the people is proportional to the number of illiterate people in the population. Letting f(t) represent the number of literate people, determine the differential equation that f(t) satisfies. (Let k represent a positive constant.)
A) $f ^ { \prime }$ (t) = $\frac { k f ( t ) } { 500,000 }$
B) $f ^ { \prime }$ (t) = 500,000(1 - f(t))
C) $f ^ { \prime }$ (t) = k(500,000 - f(t))
D) $f ^ { \prime }$ (t) = 500,000 - kf( t)
E) none of these

Question

Quizplus · Accepted Answer

The rate of increase of literacy (i.e., the rate of change of the number of literate people, $f'(t)$) is proportional to the number of illiterate people, which is $500,000 - f(t)$. Therefore, $f'(t) = k(500,000 - f(t))$.

A Certain Developing Country Has a Population of 500,000 f′f ^ { \prime }f′

A Certain Developing Country Has a Population of 500,000 $f ^ { \prime }$