Question 1046753: Let q = demand for a product and p = price in dollars charged for a product. Suppose that q = 10,000p^−4. If you wanted to "invert" this relationship to express p as a function of q, you would obtain? My workings were as follows: (1) multiple both sides by p^4, giving qp^4 = 10,000 (2) divide both sides by q, giving p^4 = 10,000/q (3) apply an exponent of 0.25 to both sides giving p = 10,000^0.25 / q^0.25, or p = 10 / q^0.25. This was wrong - where did I go wrong?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! q = demand
p = price
q = 10,000 * p^(-4)
it's probably easiest to convert everything to positive exponents before doing any converting.
p^(-4) is equal to 1/p^4.
your formula becomes q = 10,000 / p^4
multiply both sides of the equation by p^4 and divide both sides of the equation by q to get:
p^4 = 10,000 / q
take the fourth root of both sides of the equation to get:
(p^4)^(1/4) = (10,000/q)^(1/4)
simplify to get:
p = 10,000^(1/4) / q^(1/4)
simplify further to get:
p = 10 / q^(1/4).
this can also be expressed as p = 10 * q^(-1/4)
check to see if you got it right.
start with q = 10,000 * p^(-4)
since p^-4) = 1/p^4, your equation becomes:
q = 10,000 / p^4
assume that p equals any random number.
i chose p = 3.
formula becomes:
q = 10,000 / 3^4 which becomes q = 10,000 / 81 which becomes q = 123.4567901.
now start with p = 10 / q^(1/4)
when q = 123.4567901, this becomes:
p = 10 / 123.4567901^(1/4) which becomes p = 10 / (10/3) which becomes:
p = 10 * 3/10 which becomes p = 3.
since we started with p = 3 and solved for q and then used q to solve for p and got back to the original value of p, the formula and its inverse look good.
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