Write the Word or Phrase That Best Completes Each Statement $\mathrm { P } ( \mathrm { t } ) = 1 + \mathrm { ke } 0.03 \mathrm { t }$

Write the word or phrase that best completes each statement or answers the question.
-The population of a particular city is increasing at a rate proportional to its size. It follows the function $\mathrm { P } ( \mathrm { t } ) = 1 + \mathrm { ke } 0.03 \mathrm { t }$ where $\mathrm { k }$ is a constant and $\mathrm { t }$ is the time in years. If the current population is 39,000 , in how many years is the population expected to be 97,500 ?

A) $13 \mathrm { yr }$
B) $187 \mathrm { yr }$
C) $31 \mathrm { yr }$
D) $18 \mathrm { yr }$