The population P of a town has a rate of change proportional to the difference between P and 15,000. This may be expressed as dP/dt = k(P - 15000), where k = 0.2 and t = time in years. Find the population after one year

here is how I decided to do it. can someone please check?

initially,

when t = 1

this is not the answer. the answer is 22,000.

what did i do wrong?