Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable.

The rate of change of P is proportional to P$.$ When t $=0,$ P $=6,000$ and when t $=1,$ P $=5,100.$ What is the value of P when t $=6?$

Write the differential equation. $($Use k for the constant of proportionality.$)$

dP$/$dt$=$ kP

Solve the differential equation.

P $=\_\_\_\_\_\_\_\_$

Evaluate the solution at the specified value of the independent variable. $($Round your answer to three decimal places.$)$

$=2263\mathrm{.}154$