Question 1186687: The demand curve for a swivel chair is given by p=4000^(3-q) dollars per swivel chair, where p is the price and q is the quantity, in thousands of swivel chairs, demanded at that price. What quantity will be demanded if the price per swivel chair is $256.60?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to solve this problem:
1. **Write down the given information:**
* Demand curve: p = 4000^(3-q)
* Price (p) = $256.60
2. **Substitute the price into the demand equation:**
256.60 = 4000^(3-q)
3. **Solve for q:**
This equation is easiest to solve using logarithms. Let's take the logarithm (base 10 is easiest) of both sides:
log(256.60) = log(4000^(3-q))
log(256.60) = (3-q) * log(4000)
Now, isolate (3-q):
(3-q) = log(256.60) / log(4000)
(3-q) ≈ 2.4093 / 3.6021
(3-q) ≈ 0.6688
Solve for q:
q = 3 - 0.6688
q ≈ 2.3312
4. **Interpret the result:**
q represents the quantity in *thousands* of swivel chairs. Therefore, the quantity demanded is approximately 2,331 swivel chairs.
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