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
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
2.
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
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.
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