jessicawade
  • jessicawade
linear transformation model help
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  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jessicawade
  • jessicawade
Number of months Number of fish 0 8 1 39 2 195 3 960 4 4,738 5 23,375
jessicawade
  • jessicawade
log y hat=0.9013x+0.6935
jessicawade
  • jessicawade
Use the linear transformation model to predict the number of fish in 12 months.

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jessicawade
  • jessicawade
i got 5,685,367
jessicawade
  • jessicawade
@atreyu6s3x6
anonymous
  • anonymous
haha sorry im bad at prob and stats
mathmate
  • mathmate
The model is way off even at 5 months. Can you double-check the model?
anonymous
  • anonymous
i think @mathmate has it haha
jessicawade
  • jessicawade
hmmm thats what i got
jessicawade
  • jessicawade
(log y hat=0.9013•logx+ 0.6935 ) this the other model thats is the closest to the one i have
jessicawade
  • jessicawade
but im pretty sure my log is correct
jessicawade
  • jessicawade
I have this question and the other one @atreyu6s3x6 tried helping me with. i can show you the entire part of the lesson if you need it.
jessicawade
  • jessicawade
Scientists are studying the population of a particular type of fish. The table below shows the data gathered over a five–month time period. Use the data to answer questions 5–9. Number of months Number of fish 0 8 1 39 2 195 3 960 4 4,738 5 23,375 5. What does the scatterplot of the data show? (1 point) • a strong positive linear relationship • a strong negative linear relationship • a curve that represents exponential growth * • a curve that represents exponential decay 6. Complete an exponential transformation on the y-values. What is the new value of y when x = 5? (1 point) • 4.3688 • 3.6756 * • 0.6990 • 3.3757 7. Find the linear transformation model. (1 point) • logy hat=o.6935•logx+ 0.9013 • log y hat=0.9013x+0.6935* • log y hat=0.6935x+ 0.9013 • log y hat=0.9013•logx+ 0.6935 8. Use the linear transformation model to predict the number of fish in 12 months. (2 points)
jessicawade
  • jessicawade
i put a * next to my answers
mathmate
  • mathmate
It is much clearer when you post the complete original post. If you post your answer as part of the question, it will make the question inconsistent. First, do you think it is a linear or exponential relationship?
jessicawade
  • jessicawade
well i think its linear because when the x values increase so do the y values
jessicawade
  • jessicawade
JUST KIdding
jessicawade
  • jessicawade
its an exponential growth lol
mathmate
  • mathmate
exactly! What have you learned about transformation?
jessicawade
  • jessicawade
not sure, i have taken notes but i lost the notebook earlier yesterday
mathmate
  • mathmate
Do you have a textbook?
jessicawade
  • jessicawade
no im on online school
mathmate
  • mathmate
You cannot go back to the lessons?
jessicawade
  • jessicawade
I can but they wont explain everything once i pass the lesson just bits
jessicawade
  • jessicawade
so i got log y hat=0.9013x+0.6935 as the transformation model out of the answers, but im not sure how to find the number of fish after 12 months, which is confusing me lol
mathmate
  • mathmate
ok, are you looking for the answer or are you looking to understand?
jessicawade
  • jessicawade
understand please
mathmate
  • mathmate
We'll rewind to the beginning, ok?
jessicawade
  • jessicawade
ok
mathmate
  • mathmate
Typically, a linear model has the form y=ax+b but that's not our case.
jessicawade
  • jessicawade
ok
mathmate
  • mathmate
Similarly, an exponential growth model has the form \(y=ax^{bx}\) where a and b are to be found.
mathmate
  • mathmate
so far so good?
jessicawade
  • jessicawade
yes
mathmate
  • mathmate
However, the parameters a and b are hard to calculate directly from the exponential model. Since we (including you) already know how to model a straight line, we will transform the exponential to a straight line. Then we'd find the parameters as though it is a straight line.|dw:1447097415267:dw| That's where transformation comes in.
mathmate
  • mathmate
@jessicawade are you still there?
jessicawade
  • jessicawade
yeah my computer wasnt laoding
jessicawade
  • jessicawade
ohhhh ok :)
mathmate
  • mathmate
The way the transformation works is you would take log (to base 10 in your case) on both sides. Can you do that for me?
mathmate
  • mathmate
Take log on both sides of \(y=ax^{bx}\)
jessicawade
  • jessicawade
let me try im not very good at math
jessicawade
  • jessicawade
so on both sides on the y and the ax?
jessicawade
  • jessicawade
i dont get it xD
jessicawade
  • jessicawade
@mathmate
mathmate
  • mathmate
\(y=ax^{bx}\) actually should read \(y=a(10)^{bx}\)........ if we take log 10 eventually We'll take log on both sides, so \(log(y)=log(ax^{bx})=log(a)+log(10^{bx})=log(a)+bx~log(10)=bx+log(a)\) This is done by the laws of logarithm (which you'll need to brush up for this course) Put it simply, \(log(y)=bx+log(a)\).........where a and b are constants to be found for the given data set.
mathmate
  • mathmate
So we just finished the transformation part. Except for the laws of logarithm, are you following with the concept?
jessicawade
  • jessicawade
yeah so far i think haha
mathmate
  • mathmate
It turns out that the constant "a" is the initial value, or the y-intercept.What is the y-intercept in our problem?
jessicawade
  • jessicawade
is that the same as log y?
mathmate
  • mathmate
|dw:1447098799871:dw| "a", the y-intercept is the value of y when x=0. In our case, a=8 becase the number of fish is 8 at month 0.
jessicawade
  • jessicawade
ohhhhhhh!!!
jessicawade
  • jessicawade
so a and y are basically the same thing
mathmate
  • mathmate
So what is now our equation? from \(log(y)=bx+log(a)\) becomes?
jessicawade
  • jessicawade
so we just have to find the number of fish in 12 months, that doesnt seem hard but i dont know how to find it lol
mathmate
  • mathmate
You need to know (or confirm) that you're using the right model before you can find the number of fish at 12 months, right?
mathmate
  • mathmate
Can you find what is log(8)?
jessicawade
  • jessicawade
correct, so thats what were trying to do right? find the correct model, or try to see if mine is correct
mathmate
  • mathmate
We'll know if we're finding one or confirming one after the next step. Can you find the value of log(a)=log(8)?
jessicawade
  • jessicawade
hold on sec
jessicawade
  • jessicawade
no ium stuck
jessicawade
  • jessicawade
because isnt a=8
jessicawade
  • jessicawade
sorry im being complicated.. lol
mathmate
  • mathmate
a=8 is right, but we need log(8) in the model. If you don't have a calculator, google log(8).
jessicawade
  • jessicawade
ok
jessicawade
  • jessicawade
its 0.90308998699
mathmate
  • mathmate
Good, so let's call it 0.9031. So the model now becomes: log(y)=bx+0.9031 Can you now go back to the list of 4 models and check which one is appropriate?
jessicawade
  • jessicawade
yeah none has y=0.931
jessicawade
  • jessicawade
i mean 0.9031
mathmate
  • mathmate
Well, remember that y_hat is just approximate estimation of y, so 0.9031 and 0.9013 are close enough for a model. Can you decide which one fits the bill? There is only one that fits (approximately) the model: log(y)=bx+0.9031 where b is a constant to be found (but will be provided by the model we choose).
jessicawade
  • jessicawade
hmmm
jessicawade
  • jessicawade
• log y hat=0.9013x+0.6935* • log y hat=0.9013•logx+ 0.6935
jessicawade
  • jessicawade
both the y= 0.913 but im not sure
mathmate
  • mathmate
• logy hat=o.6935•logx+ 0.9013 • log y hat=0.9013x+0.6935* • log y hat=0.6935x+ 0.9013 • log y hat=0.9013•logx+ 0.6935 Here are the four choices to match log(y_hat)=bx+0.9031 You need to match the constant (at the end). That leaves you with two choices, which two?
mathmate
  • mathmate
A constant is a number which is not multiplied with a variable (x, or y)
jessicawade
  • jessicawade
ohhh
jessicawade
  • jessicawade
a and c
jessicawade
  • jessicawade
so logy hat=o.6935•logx+ 0.9013 or log y hat=0.6935x+ 0.9013
mathmate
  • mathmate
Good, now look carefully, which model out of the first and third resembles our model closely?
jessicawade
  • jessicawade
log y hat=0.6935x+ 0.9013
jessicawade
  • jessicawade
so 3
mathmate
  • mathmate
Exactly, that fits what you chose earlier, however you chose it. So we've got a model, right?
jessicawade
  • jessicawade
yeah now we need to find the number of fish in 12 months
mathmate
  • mathmate
We're almost there, just one more step.
jessicawade
  • jessicawade
ok!
mathmate
  • mathmate
we now have the model log y hat=0.6935x+ 0.9013 Using the inverse transformation (i.e. transform back), we need to use the law of logarithms again to get: y_hat = 10^(0.6935x+0.9013) But whenever we work with a model, we need to check it out. We'll check for x=0, y_hat(0)=10^(0.6935x+0.9013)=10^(0.6935*0+0.9013)=7.967, close enough to 8 that we're expecting. We need to check another one, say x=5 months, can you do that?
jessicawade
  • jessicawade
let me try
jessicawade
  • jessicawade
plug in 5 for x?
mathmate
  • mathmate
exactly!
jessicawade
  • jessicawade
i cant calculate it
jessicawade
  • jessicawade
its not giving me an answer lol
mathmate
  • mathmate
type this in google 10^(0.6935*5+0.9013)
mathmate
  • mathmate
lol you still need to learn to use your calculator!
jessicawade
  • jessicawade
ohhh lol *facepalm*
mathmate
  • mathmate
what, it didn't work?
jessicawade
  • jessicawade
i got 23377.6041227
mathmate
  • mathmate
is this close to what was expected for 5 days?
jessicawade
  • jessicawade
the first part yes lol
mathmate
  • mathmate
* months, not days lol Now you're ready for the plunge..... calculate in the same way what you expect to see in 12 months.
jessicawade
  • jessicawade
so i got 1,672,245,362 o_o
mathmate
  • mathmate
Yes, it's a big number, and of course a very optimistic estimate. There will not be enough food for all the fish. But....mathematically you're right! yay!
jessicawade
  • jessicawade
yay!!! lol
jessicawade
  • jessicawade
ok i hhave 1 more
mathmate
  • mathmate
One last word! Please 1. learn to use your calculator, using powers and log 2. learn the laws of exponents and logarithms.
mathmate
  • mathmate
I have to go,but I can give you hints to get started, how's that?
jessicawade
  • jessicawade
ok!
mathmate
  • mathmate
I suggest you start a new post, so others may be able to help as well.
jessicawade
  • jessicawade
i tagged you in one, i have 2 people helping me but they are confusing me lol
mathmate
  • mathmate
ok, I'll see what I can do!

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