In a Certain Country, the Rate of Increase of the Population

Multiple Choice

In a certain country, the rate of increase of the population is proportional to the population P(t) . In fact, $P ^ { \prime } ( t ) = 0.23 P ( t )$ Suppose that initially the country's population is 50,000, and that 10 years later there are 500,000 people. Which of the following equations expresses this information mathematically?

A) 10 = $e ^ { 2.3 t }$
B) 500 = $e ^ { 2.3 ( 50 ) }$
C) 500,000 = $\mathrm { e } ^ { 0.23 ( 10 ) }$
D) 500,000 = 50,000 $e ^ { 2.3 }$
E) none of these