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MY NOTE

A college student works for $8$ hours without a break, assembling mechanical components. The cumulative number of components she has assembled after $h$ hours can be modeled $q(h)=\frac{70}{1+11\mathrm{.}55e^{-0\mathrm{.}654h}}$ components.

$($Note: Use technology to complete the question.$)$

$($a$)$ When was the number of components assembled by the student increasing most rapidly? $($Round your answer to three decimal places.$)$ hours

$($b$)$ How many components were assembled at that time? $($Round your answer to one decimal place.$)$ components

What was the rate of change of assembly at that time? $($Round your answer to three decimal places.$)$

$$ components per hour

$($c$)$ How might the employer use the information in part $($a$)$ to increase the student's productivity?

The student may only work certain days of the week to make sure productivity stays high.

The student's employer may have the student rotate to a different job before the calculated amount of time.

The student's employer may set a higher quota for the calculated amount of time.

The student's employer may wish to enforce a break after the calculated amount of time to prevent a decline in productivity.

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