calulus questions

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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

 

 

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
 
3.
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.

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