A worker having no experience with a particular process can assemble $60$ units of a product each week. After training and $t$ weeks of experience, a worker can assemble the units at the rate of

$N^{\text{'}}(t)=720e^{-4t}$

units per week.

a$.$ Specify the function that describes the worker's weekly output.

$N(t)=$

b$.$ Find the number of units a worker having $5$ weeks of experience can assemble. Round to the nearest whole number.

units per week

c$.$ What is the maximum number any worker can be expected to assemble per week? Round to the nearest whole number.

$($Hint: When you verbalize this to yourself, it should spark the thought of a limiting value. You can answer this question by taking the proper limit$.)$

units per week