Unit $4$ Case Study $1$: Emplovee Training

A payroll software firm has implemented a training program for new employees, who will be providing in person service to their clients. The trainees undergo a product knowledge test periodically during their training period. The average percentage score on this test, $P(t),$ as function of time, $t$ in weeks of training, is given by the following logistic growth function:

$P(t)=\frac{100}{1+9e^{-0\mathrm{.}5t}}$

A minimum score of $85\%$ is expected before an employee can be considered to have completed their training and capable of providing service to clients.

Questions for Investigation: Consider this scenario and develop $3$ significant questions that you would like to answer in your analysis.

Analysis and Interpretation: Write a one$-$page analysis and interpretation of this problem, using all the mathematics tools that you have learned in this unit. Include a properly labeled graph and be sure to answer the $3$ investigation questions posted above, if possible.