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

t=1935-1980= -45 


3350=2500e^(k*(-45)) 

e^(k*(-45))=3350/2500 


ln(e^(k*(-45)))=ln(3350/2500) 

k=ln(3350/2500)/(-45)=-0.0065 


In 2000 t=20, so... 


P=2500e^(-0.0065*20)= 2196 

:)