Given: dp/dt = k(m- p)
where p(t) measures the performance of someone learning a skill after a training time t, m is the maximum level of performance, and k is a positive constant. solve this differential equation to find an expression for p(t). (use p for p(t). assume that p(0) = 0.)

Step-by-step explanation:

The relation between the variables is given by

This is a separable differential equation. Rearranging terms:

Multiplying by -1

Integrating

Where D is a constant. Applying expoentials

Where , another constant

Solving for P

With the initial condition P=0 when t=0

We get C=-M. The final expression for P is

Keywords: performance , learning , skill , training , differential equation

step-by-step explanation:

6.48/4 4 goes into 6.48 1.62 times