It is estimated that the weekly output at a certain plant is Q(x) = 50x² + 9,000x units, where x is the number of workers employed at the plant. Currently there are 30 workers employed at the plant.

a. Use calculus to estimate the change in the weekly output that will result from the addition of 1 worker to the force.

b. Compute the actual change in output that will result from the addition of 1 worker.