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

question 364

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) \(18 \mathrm { yr }\)