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**differentiate** **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?

$\displaystyle P = 15,000 + Ae^{0.2t}$

initially,

$\displaystyle 21,000 = 15,000 + Ae^{0.2t}$

$\displaystyle 6,000 = Ae^{0}$

$\displaystyle 6,000 = A $

$\displaystyle P = 15,000 + 6000e^{0.2t} $

when t = 1

$\displaystyle P = 15,000 + 6000e^{0.2} $

$\displaystyle = 22328$

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

what did i do wrong?