In 1973, J. B. Keller published a theory of competitive running, in which he proposed that the speed of a sprinter (up to 300 meters) could be modeled by the differential equation

**dv/dt = A - v/b**,

where **v(t)** is the speed at time **t**. At the time of Keller's work, reasonable values for the constants were **A = 12.2** m/sec^{2} and **b = 0.892** sec.

- What is an appropriate initial condition for the model?
- Solve the initial value problem symbolically, using the parameters
**A**and**b**-- don't substitute numbers yet. You should be able to do this step with pencil and paper, but use your helper application if you need to. [You may have encountered problems of this type in many different contexts: RL circuits, Newton's Law of Cooling, exponential growth and decay, velocity in a resisting medium, and mixing problems.] - What is the limiting behavior of
**v**as**t**becomes large? What meanings can you attach to the parameters**A**and**b**?