The Population of a Particular City Is Increasing at a Rate

Multiple Choice

The population of a particular city is increasing at a rate proportional to its size. It follows the function $\mathrm{P}(\mathrm{t}) =1+\mathrm{ke} 0.08 \mathrm{t}$ where $\mathrm{k}$ is a constant and $\mathrm{t}$ is the time in years. If the current population is 12,000 , in how many years is the population expected to be 30,000 ? (Round to the nearest year.)

A) $11 \mathrm{yr}$
B) $69 \mathrm{yr}$
C) $6 \mathrm{yr}$
D) $5 \mathrm{yr}$