The populations P (in thousands) of a certain city from 2000 through 2008 can be modeled by P = 295.84ekt,where t is the year, with t = 0 corresponding to 2000. In 2006, the population was about 365,000.
(a) Find the value of k for the model. Round your result to four decimal places.
k = __________

(b) Use your model to predict the population in 2015. (Round your answer to the nearest person.)
P = ___________ thousand

Question

The populations P (in thousands) of a certain city from 2000 through 2008 can be modeled by P = 295.84ekt,where t is the year, with t = 0 corresponding to 2000. In 2006, the population was about 365,000. 
(a) Find the value of k for the model. Round your result to four decimal places.
k =  __________

(b) Use your model to predict the population in 2015. (Round your answer to the nearest person.)
P =  ___________ thousand

tkhunny · Answer

(a) $$P(6) = 295.84\cdot e^{k\cdot (6)} = 365,000$$  Solve for 'k'.

(b) I am very suspicious of this question.  We are told that the model is valid on [2000,2008].  Why, then, are we asked to produce a value for 2015?  It makes no sense.

anonymous · Answer

I think it means 'predict' as in use the available model (which matches up with the data) to extrapolate it, further...? Just a guess.

tkhunny · Answer

@ LolWolf I, too, am sure that's what it means, but it would be wrong not to object to the question a little.  We should have at least a small expectation that the model is, or may be, valid where we use it.