Solve the Problem $\mathrm { P } ( \mathrm { t } ) = 1 + \mathrm { ke } ^ { 0.05 \mathrm { t } }$

Multiple Choice

Solve the problem.
-The population of a particular city is increasing at a rate proportional to its size. It follows the function $\mathrm { P } ( \mathrm { t } ) = 1 + \mathrm { ke } ^ { 0.05 \mathrm { t } }$ where $\mathrm { k }$ is a constant and $\mathrm { t }$ is the time in years. If the current population is 36,000 , in how many years is the population expected to be 90,000 ? Round to the nearest year.

A) $8 \mathrm { yr }$
B) $121 \mathrm { yr }$
C) $10 \mathrm { yr }$
D) $18 \mathrm { yr }$