Demographic Studies Conducted in a Certain City Indicate That the Fraction

Multiple Choice

Demographic studies conducted in a certain city indicate that the fraction of the residents that will remain in the city for at least t years is $f ( t ) = e ^ { - t / 50 }$ .The current population of the city is 500,000,and it is estimated that new residents will be arriving at the rate of 1,000 people per year.If this estimate is correct,what will be the population in the long run?

A) 40,800
B) 50,000
C) 550,000
D) 40,500