Question

I give medals and fans!!

Please help me!!!!

Suppose you plan to buy many blank compact disks. You check price lists and find out that if you buy 100 CDs or fewer you pay $0.74 each. However if you buy between 100 and 300 CDs the price drops to $0.69 each for the second hundred. Write a function that describes the cost c of n number of CDs purchased.

Answer 1

Two questions:1) Does that mean that any CDs bought after 300 is also $0.69 as well?
2) Is every CD bought between 100 and 300 $0.69? Sorry, just a little confused with the wording.

If that is the case, then the answer might be a piecewise function. Let me brush up on that for a sec.

Answer 2

Yes to both questions.(: and alrighty!

Answer 3

I meant like I can become your fan.

Answer 4

So here we want to relate the cost with the number of CDs purchased. This is the same concept as with x and y functions. First we want to decide which of the two variables is dependent, and which is independent. Just in case you didn't notice before, when we say "f(x)=...", we are observing how changing the independent variable (x in this case) affects the dependent (y in this case). We decide how many CDs are bought, so that would be our x variable, while the cost would be our y, since the cost depends on the number of CDs purchased.

Feel free to use your own variables!

Let f(x)=cost
Let x=number of CDs purchased

Since the first 100 CDs will cost us $.74, we can use the equation:
f(x)=.74x [or you can replace f(x) with y]

Then anything after is discounted to $.69, so the equation for this is:
f(x)=.69x

Now that we have our equations, all that is left to do is to put them into the proper piecewise format:
f(x)={.74x when 0≤x≤100
.69x when 101≤x≤300

Just imagine that the bracket extends down to cover the .69x as well, and there's your answer. Sorry for the lengthy response, I like to explain my thought process.

Answer 5

Thank you so much! The explanation helped me, so the lengthy response is perfectly fine! Thank you again.(: