Let $\displaystyle {P}{\left({t}\right)}$ be the performance level of someone learning a skill as a function of the training time $\displaystyle {t}$. The derivative $\displaystyle {\frac{{{d}{P}}}{{{\left.{d}{t}\right.}}}}$ represents the rate at which performance improves. If $\displaystyle {M}$ is the maximum level of performance of which the learner is capable, then a model for learning is given by the differential equation
$\displaystyle {\frac{{{d}{P}}}{{{\left.{d}{t}\right.}}}}={k}{\left({M}-{P}{\left({t}\right)}\right)}$
where $\displaystyle {k}$ is a positive constant.
Two new workers, John and Peter, were hired for an assembly line. John could process $\displaystyle {11}$ units per minute after one hour and $\displaystyle {15}$ units per minute after two hours. Peter could process $\displaystyle {10}$ units per minute after one hour and $\displaystyle {16}$ units per minute after two hours. Using the above model and assuming that $\displaystyle {P}{\left({0}\right)}={0}$, estimate the maximum number of units per minute that each worker is capable of processing.
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Peter: Preview Question 6 Part 2 of 2   .