Variation Functions

[dragonicneos]

Need help on these questions
16. 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.
a. based on these figures how could you expect the price of a diamond to vary with its weight (number of carats)?
b. Predict the price of
i) a 3 carat diamond
ii) a 1/4 carat diamond
c. write the particular equation expressing the number of dollars in terms of the number of carats.
d. the hope diamond weighs 44.5 carats. Based on your model, how much should it be worth?
e. Approximately how large a diamond could you get for $2000?
f. The weights of similarly shaped diamonds are directly proportional to the cubes of their diameters. Wirte a general equation expressing this fact.
g. Substitute the expression for weight from part f into the equation for price in partc, and simplify as much as possible. Then tell how the price of a diamond vaires with its diameter.
h. If a particular diamond costs $500, how much would you expect to pay for one with twice the diameter?

 

[Denis]

Show your work: we can't tell where you need help.
Read "Read before posting".

 

[dragonicneos]

i just dont know how to make the equation so i can solve the rest of the other stuff
so im kinda stuck

 

[mmm4444bot]

What types of variation have you studied?

 

[dragonicneos]

direct and inversely

 

[dragonicneos]

what i really dont understand about this equation is the particular equations expressing $ in terms of carats
because they give you two points ($360,.75carat) and ($1440, 1.5carat) and they arent similar so im not sure how to solve it
heres what i got
360=k(3/4) k=480
1440=k(1.5) k=960
so something tells me that this equation is exponential (or at least i think)
anyone have a solution?

 

[dragonicneos]

okay i think i found the particular equations its
square root of $=k times c
$=cost
c=carats

 

[mmm4444bot]

\(\displaystyle \sqrt{V} \;=\; k \cdot c\)

\(\displaystyle \text{V = value in dollars}\)

\(\displaystyle \text{c = weight in carats}\)

This shows quadratic behavior, not exponential. It's a fine model, if a quadratic function is an acceptable choice for this exercise.

I find it peculiar that they ask for the predictions in part (b) before finding the relationship in part (c). I sense that something is amiss.

Can you solve for k?

If so, substitute your value for k into the equation above, and square both sides to get a function for V in terms of c.

That would be part (c).

Parts (d) and (e) easily follow.

Part (f) requires that you first define a symbol for the gem's diameter. I'm thinking that you'll need to state another constant of variation, too. You could use K instead of k, since k is already taken.

Hmmm. That's going to make part (g) a bit messy, I think.

Please double-check that you've correctly posted the entire exercise.

Are you taking an on-line math course?