alg2 trig

[mollymurphy]

16. Diamond Problem A discount diamond house ran an ad in a local newspaper which showed a 3/4 carat diamond for $360 and a 1.5 carat diamond for $1440.

question: Assuming that the price of a diamond varies with some power of its weight, write the particular equation.

 

[tkhunny]

Definitions:

P = Price of Diamond
W = Weight of Diamond.

Drive this into your head. {something} varies with {something else} MEANS {something} = k{something else}. When encountering such a thing, just write down the equation.

"the price of a diamond varies with some power of its weight" ==> \(\displaystyle P = k\cdot W^{n}\)

This problem is a little unusual, as we ahve more the 'k' to find. No matter. Substitute both known cases and solve for both missing pieces.

Let's see what you get.

 

[mmm4444bot]

the price of a diamond varies directly with some power of its weight

{something} varies directly with {something else} MEANS {something} = k{something else}

"the price of a diamond varies directly with some power of its weight" ==> \(\displaystyle P = k\cdot W^{n}\)


The adverb "directly" clarifies the type of variation.

Common sense tells us that the variation is direct (versus inverse), in this exercise; yet, considering good form, I think that the given information should have explicitly stated the type of variation.