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 = 2,000 and when t = 1, P = 1,500. What is the value of P when t = 4? Write the differential equation. (Use k for the constant of proportionality.) dP dt = Solve the differential equation. P = Evaluate the solution at the specified value of the independent variable. (Round your answer to three decimal places.)

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