Choose the One Alternative That Best Completes the Statement or Answers

Multiple Choice

Choose the one alternative that best completes the statement or answers the question.
-The population of a particular city is increasing at a rate proportional to its size. It follows the function $P ( t ) = 1 + k e ^ { 0.03 t }$ where k is a constant and t is the time in years. If the current population
Is 47,000, in how many years is the population expected to be 117,500?

A) 31 yr
B) 193 yr
C) 18 yr
D) 13 yr