The population P (in thousands)of Reno,Nevada from 2000 through 2007 can be modeled by $P = 346.8 e ^ { k t }$ where t represents the year,with $t = 0$ corresponding to 2000.In 2005,the population of Reno was about 395,000.According to the model,during what year will the population reach 486,000.00?
A)2013
B)2005
C)2021
D)2017
E)2009

Question

The population P (in thousands)of Reno,Nevada from 2000 through 2007 can be modeled by $P = 346.8 e ^ { k t }$ where t represents the year,with $t = 0$ corresponding to 2000.In 2005,the population of Reno was about 395,000.According to the model,during what year will the population reach 486,000.00? ​
A)2013
B)2005
C)2021
D)2017
E)2009

Quizplus · Accepted Answer

To find the year when the population will reach 486,000, we first need to solve for the value of $k$ using the given information for 2005. In 2005 ($t = 5$), the population was about 395,000, or 395 in thousands. Substituting these values into the equation gives us $395 = 346.8e^{5k}$. Solving for $k$ gives us $k \approx 0.0262$.Next, we use the population value of 486,000 (or 486 in thousands) to find the year. Substituting into the equation $486 = 346.8e^{kt}$ and using the value of $k$ we found, we solve for $t$. This gives us a value of $t \approx 13$.Since $t = 0$ corresponds to the year 2000, $t = 13$ corresponds to the year 2013.

The Population P (In Thousands)of Reno,Nevada from 2000 Through 2007 P=346.8ektP = 346.8 e ^ { k t }P=346.8ekt

The Population P (In Thousands)of Reno,Nevada from 2000 Through 2007 $P = 346.8 e ^ { k t }$