1) Pure Water Enterprises finds that the marginal profit, in dollars, from drilling a well that is x feet deep is given by

P?(x)=5x? Find the profit when a well 250 ft deep is drilled.

- A company is producing a new product. Due to the nature of the product, the time required to produce each unit decreases as workers become more familiar with the production procedure. It is determined that the function for the learning process is

T(x)=2+0.3(x1?)

where T(x) is the time, in hours, required to produce the xth unit.

Use this information for Exercises 2 and 3.

2) Find the total time required for a new worker to produce units 1 through 10; units 20 through 30.

3) Find the total time required for a new worker to produce units 1 through 20; units 20 through 40.

4) Suppose that in a memory experiment the rate of memorizing is given by

M?(t)=?0.009t2+0.2t

Where M'(t) is the memory rate, in words per minute. How many words are memorized in the first 10 min (from t=0 to t=10)?

Memorizing. The rate of memorizing information initially increases. Eventually, however; a maximum rate is reached, after which it begins to decrease. Memory rate (in words per minute) O 10 t Time (in minutes)