SOLUTION: Good Day, Got no reply to this question. 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 tho

Question 1186829: Good Day,
Got no reply to this question.
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?
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

The demand curve for a swivel chair is given by:

given: the price per swivel chair is $

.....take log of both sides

thousands of swivel chairs

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the demand curve formula is:

p = 4000 ^ (3 - q)

p is the price per swivel charge.
q is the number of 1000 swivel chairs.

when the price is 256, the formula becomes:

256 = 4000 ^ (3 - q)

take the log of both sides of this equation to get:

log(256) = log(4000 ^ (3 - q))

since log(4000 ^ (3 - q)) is equal to (3 - q) * log(4000), the equation becomes:

log(256) = (3 - q) * log(4000)

divide both sides of this equation by log(4000) to get:

log(256) / log(4000) = 3 - q

add q to both sides of this equation and subtract log(256) / log(4000) from both sides of this equation to get:

q = 3 - log(256) / log(4000).

solve for q to get:

q = 2.331427025.

that should be your solution.

confirm by replacing q in the original equation to get:

p = 4000 ^ (3 - q) becomes:

p = 4000 ^ (3 - 2.331427025)

solve for p to get:

p = 256.

your solution is confirmed to be good.

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