Question

Write a function that models the data set?

Answer 1

Please help with these two questions! I've been stuck on them for at least an hour! I have some work to show for the first one but I'm really lost on the second one. Any help would be appreciated..
http://imgur.com/MfPXdeB

Here is my work for the first one:
y2-y1/x2-x1;
(0.125 - 512) / (5 + 7)
-511.875 / 12
-42.656 ~ -43

y - y1 = m(x - x1)
y - 512 = -42(x + 7)
y - 512 = -42x -294

y = -42x + 218
f(x) = -42x + 218

Is it correct?
Thanks a lot in advanced for your help!

Answer 2

What's the difference between each value of \(x\) in the first table?

Answer 3

Well, here's a hint: figure out the difference between adjacent values of \(x\) in the table. Then look at the ratio between adjacent values of \(y\) in the table. I think you'll find that the ratio is expressed as some number to the difference in \(x\).

For the second one, taking the log of the number of shares appears to make the data fit a straight line pretty well.

Answer 4

@whpalmer4 - there's a difference of 3 in each value of x in the first table.
I tried that and that's how I got the answer for the first one... I don't think it's right though. /:

How would we take the log of the number of shares? How could we write that in an expression?
I'm sorry for being so lost. I guess I'm just really stressed out over this. Believe me, I'm usually not this stingy or desperate for help. :(

Answer 5

Looking at the first table, every entry, \(x\) decreases by 3. Now what is the ratio between the values of \(y\) as \(x\) decreases by 3?

For the second problem, instead of plotting shares in billions vs. year, you plot the logarithm of shares in billions vs. year. They even make graph paper which has a logarithmic scale to facilitate doing this—you just plot the points as normal, except that the spacing of the lines on the paper changes, giving you the same effect.

Answer 6

to take the logarithm of the number of shares, you'll enter the number of shares into your calculator, then press the Log button. Here's what the first few data points would be:

\[\begin{array}{|l|c|r|}
\hline
\text{Years since 1949}&\text{Shares (in billions)}&\text{Log (Shares in billions)}\\
\hline
1&2.4&0.380211\\
\hline
11&6.5&0.812913\\
\hline
21&16.1&1.20683\\
\hline
\end{array}\]

Here's a plot of the entire table, along with a best-fit line through the points. You can see that the straight-line fit through the log of the data is rather good.

Answer 7

@whpalmer4 - Thank you for helping.. But I need to write a function for the first one. This is the third day and I'm still stuck on this. I'm about to give up and I don't know WHY I STILL can't get this. UGH. I am so flustered.

I need to write a function for the second one too and then just input the values my instructor is asking for. I'm going to look at some review and see if it helps at all. I'm really lost.

Answer 8

You can't write a function until you have determined the relationship. I'm asking you questions that will guide you to that relationship, if you cooperate and answer them.

Answer 9

@whpalmer4 - I'm honestly getting more lost through all of this though. My teacher provided us with notes but none of them have included anything about the relationship between both in this case. Or logging. We've only found out about first and second differences so far. That's why I'm so confused, because I'm honestly clueless on the information you're trying to give me. I apologize.

Answer 10

I'll ask the question again. What is the ratio between successive values of \(y\) in the table of data for the first question?

\begin{array}{|l|c|r|}
\hline
x & -7 & -4 & -1 & 2 & 5\\
\hline
y & 512 & 64 & 8 & 1 & 0.125\\
\hline
\end{array}

Answer 11

As \(x\) goes from \(-7\) to \(-4\), \(y\) goes from \(512\) to \(64\). What is the quotient of \(512/64\)?

As \(x\) goes from \(-4\) to \(-1\), \(y\) goes from \(64\) to \(8\). What is the quotient of \(64/8\)?

As \(x\) goes from \(-1\) to \(-2\), \(y\) goes from \(8\) to \(1\). What is the quotient of \(8/1\)?

Do you see a pattern here? Does it continue through the rest of the data?