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1. The demand for personal computers in the home goes up with household income. For a given community, we can approximate the average number of computers in a home as

q = 0.3458 ln x − 3.043 10,000 ≤ x ≤ 125,000

where x is mean household income. Your community has a mean income of $20,000, increasing at a rate of $2,500 per year. How many computers per household are there? (Round your answer to four decimal places.)
________computers per household

How fast is the number of computers in a home increasing? (Round your answer to four decimal places.)
________computers per household per year

You can now sell 70 cars per month at $35,000 per car, and demand is increasing at a rate of 3 cars per month each month. What is the fastest you could drop your price before your monthly revenue starts to drop? HINT [Revenue = Price × Quantity.]

dp/dt = $________per month

A point is moving along the circle x² + (y − 5)² = 2 in such a way that its x-coordinate is decreasing at a rate of 3 unit per second. What is happening to the y-coordinate at the instant when the point has reached

(−1, 6). The y-coordinate is _____________at a rate of ___________ units per second.