The population P (in thousands)of Orlando,Florida from 2000 through 2007 can be modeled by $P = 1530.6 e ^ { k t }$ where t represents the year,with $t = 0$ corresponding to 2000.In 2006,the population of Orlando,Florida was about 1,883,000.00.Find the value of k.
A)k = 0.03183
B)k = 0.02863
C)k = 0.02163
D)k = 0.03453
E)k = 0.03063

Question

The population P (in thousands)of Orlando,Florida from 2000 through 2007 can be modeled by $P = 1530.6 e ^ { k t }$ where t represents the year,with $t = 0$ corresponding to 2000.In 2006,the population of Orlando,Florida was about 1,883,000.00.Find the value of k. ​
A)k = 0.03183
B)k = 0.02863
C)k = 0.02163
D)k = 0.03453
E)k = 0.03063

Quizplus · Accepted Answer

We can use the given model, P(t) = 1000e^(kt), to find the value of k by using the given information that P(6) = 1883000.

So, we have:

P(6) = 1000e^(6k) = 1883000

Dividing both sides by 1000, we get:

e^(6k) = 1883

Taking natural logarithm on both sides, we get:

ln(e^(6k)) = ln(1883)

Simplifying, we get:

6k = ln(1883)

Therefore, the value of k is:

k = ln(1883)/6 = 0.03453

Therefore, the best choice that matches with the calculated value of k is D.

The Population P (In Thousands)of Orlando,Florida from 2000 Through 2007 P=1530.6ektP = 1530.6 e ^ { k t }P=1530.6ekt

The Population P (In Thousands)of Orlando,Florida from 2000 Through 2007 $P = 1530.6 e ^ { k t }$