Question

linear transformation model help

Answer 1

Number of months Number of fish
0 8
1 39
2 195
3 960
4 4,738
5 23,375

Answer 2

log y hat=0.9013x+0.6935

Answer 3

Use the linear transformation model to predict the number of fish in 12 months.

Answer 4

i got 5,685,367

Answer 5

@atreyu6s3x6

Answer 6

haha sorry im bad at prob and stats

Answer 7

The model is way off even at 5 months. Can you double-check the model?

Answer 8

i think @mathmate has it haha

Answer 9

hmmm thats what i got

Answer 10

(log y hat=0.9013•logx+ 0.6935 ) this the other model thats is the closest to the one i have

Answer 11

but im pretty sure my log is correct

Answer 12

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.

Answer 13

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)

Answer 14

i put a * next to my answers

Answer 15

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?

Answer 16

well i think its linear because when the x values increase so do the y values

Answer 17

JUST KIdding

Answer 18

its an exponential growth lol

Answer 19

exactly!
What have you learned about transformation?

Answer 20

not sure, i have taken notes but i lost the notebook earlier yesterday

Answer 21

Do you have a textbook?

Answer 22

no im on online school

Answer 23

You cannot go back to the lessons?

Answer 24

I can but they wont explain everything once i pass the lesson just bits

Answer 25

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

Answer 26

ok, are you looking for the answer or are you looking to understand?

Answer 27

understand please

Answer 28

We'll rewind to the beginning, ok?

Answer 29

ok

Answer 30

Typically, a linear model has the form
y=ax+b
but that's not our case.

Answer 31

ok

Answer 32

Similarly, an exponential growth model has the form
\(y=ax^{bx}\)
where a and b are to be found.

Answer 33

so far so good?

Answer 34

yes

Answer 35

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.
That's where transformation comes in.

Answer 36

@jessicawade
are you still there?

Answer 37

yeah my computer wasnt laoding

Answer 38

ohhhh ok :)

Answer 39

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?

Answer 40

Take log on both sides of
\(y=ax^{bx}\)

Answer 41

let me try im not very good at math

Answer 42

so on both sides on the y and the ax?

Answer 43

i dont get it xD

Answer 44

@mathmate

Answer 45

\(y=ax^{bx}\) 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.

Answer 46

So we just finished the transformation part. Except for the laws of logarithm, are you following with the concept?

Answer 47

yeah so far i think haha

Answer 48

It turns out that the constant "a" is the initial value, or the y-intercept.What is the y-intercept in our problem?

Answer 49

is that the same as log y?

Answer 50

"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.