The population P of a city if given by
P=2500e^(kt)
where t is time of the years , with t=0 corresponding to the years 1980 .In 1935 ,the population was 3350 .Find the value of k and use this result to predict the population in the years 2000

Question

The population P of a city if given by 
   P=2500e^(kt)
where t is time of the years , with t=0 corresponding to the years 1980 .In 1935 ,the population was 3350 .Find the value of  k and use this result to predict the population in the years 2000

anonymous · Answer

I'm sorry are you sure that isn't 1985? instead of 1935??? You are beginning time with 1980 (t=0)...I'm not sure it would make sense to have t=-45 in the year 1935.  I think you have 1985.  If so then you have to plug these values into the equation:
3350=2500e^k(5)    (In 1980 time t=0 so in 1985 5 years have passed by and t is in years) Then we have
3350/2500=e^5k
ln(3350/2500)=5k
ln(3350/2500)/5=k
Now plug in k in your given equation P=2500e^(kt).  Remember you are looking for the population in the year 2000 so your t is now t=2000-1980.

anonymous · Answer

yes,I positive I think is decay because is -45 years