Solve.
-The population of a particular city is increasing at a rate proportional to its size. It follows the function $\mathrm { P } ( \mathrm { t } ) = 1 + \mathrm { ke } ^ { 0.12 \mathrm { t } }$ where $\mathrm { k }$ is a constant and $\mathrm { t }$ is the time in years. If the current population is 50,000 , in how many years is the population expected to be 125,000 ? (Round to the nearest year.)
A) $8 \mathrm { yr }$
B) $3 \mathrm { yr }$
C) $60 \mathrm { yr }$
D) $5 \mathrm { yr }$

Question

Quizplus · Accepted Answer

Given the current population is 50,000, we first find the value of $k$ by substituting $P(t) = 50,000$ and $t = 0$ (since it's the current population) into the equation $P(t) = 1 + ke^{0.12t}$. This gives us $50,000 = 1 + k$, so $k = 49,999$. To find when the population will be 125,000, we substitute $P(t) = 125,000$ and solve for $t$: $125,000 = 1 + 49,999e^{0.12t}$. Solving this equation for $t$ gives approximately 8 years.

Solve -The Population of a Particular City Is Increasing at a Rate

Solve
-The Population of a Particular City Is Increasing at a Rate