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

Multiple Choice

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