Question

Assume that after t hours on the job, a factory worker can produce 100te^-.5t units per hour. How many units does the worker produce during the first three hours?

Answer 1

The number of units produced by the worker during t hours of work can be modelled by the following function:

$N(t)=100t e^{(-0.5t)}$

To find the number of units produced during first 3 hours, we can substitute 3 for t. This will give us the number of units produced by the worker during first 3 hours.

$N(3)=100(3) e^{-0.5(3)} = 67$

Thus the worker will produce 67 units during the first 3 hours of the work.