1. ## regression

I do not even know where to begin with this problem...please help. I am in intermediate algebra, summer session, which is moving quite fast. It seems as if there is no time for understanding.

Please explain how would I know when to use log in the equation when I have a word problem and it is only asking to find an equation for f.

Also what is the base b of the function f(t)= ab^t?

How do I find regression equations?

2. Originally Posted by getnaphd
I do not even know where to begin with this problem...please help. I am in intermediate algebra, summer session, which is moving quite fast. It seems as if there is no time for understanding.

Please explain how would I know when to use log in the equation when I have a word problem and it is only asking to find an equation for f.

Also what is the base b of the function f(t)= ab^t?

How do I find regression equations?

First try to put only one question in a post, you can post any number
seperatly.

Second, can you give n example of the type of word problems you have.

Third, b is a constant in the equation which is raised to the variable power t.

Fourth. look here.

RonL

3. ## summer college math...help

Sorry for the many questions..I was frustrated and up late. Still I have had no sleep.

Here is an example:Before 1997, the Library of Congress sold copies of its 3x5 catalog cards to other libraries. Due to libraries using computer catalogs, the Library of Congress stopped selling such cards in March 1997. The number of cards sold (in millions) for various years are listed in the table below.

Year Number of Cards Sold (in millions)
1971 74.47
1976 39.82
1981 15.64
1986 8.08
1991 2.36
1996 0.57

Let f(t) represent the number of cards in millions in the year that is t years since 1970.

a) Find an equation for f.
b) Use your model to estimate the number of cards sold in 1960.
c) What is the base b of your model f(t)=ab^t? What does it mean in terms of the situation?

Thanks

4. Originally Posted by getnaphd
Sorry for the many questions..I was frustrated and up late. Still I have had no sleep.

Here is an example:Before 1997, the Library of Congress sold copies of its 3x5 catalog cards to other libraries. Due to libraries using computer catalogs, the Library of Congress stopped selling such cards in March 1997. The number of cards sold (in millions) for various years are listed in the table below.

Year Number of Cards Sold (in millions)
1971 74.47
1976 39.82
1981 15.64
1986 8.08
1991 2.36
1996 0.57

Let f(t) represent the number of cards in millions in the year that is t years since 1970.

a) Find an equation for f.
b) Use your model to estimate the number of cards sold in 1960.
c) What is the base b of your model f(t)=ab^t? What does it mean in terms of the situation?

Thanks
You are going to do a power law fit. The model is of the form:

$
f(t)=a~b^t
$

Now we know how to do linear regerssion so we want to convert this lo a linear model, so we take logs to get:

$
\log(f(t))=b \log(t)+log(a)
$

so we put $\tau = \log(t)$, $F(\tau)=\log(f(e^t))$, and [tex]\alpha=log(a) , which gives us the linear model:

$
F(\tau)=b\ \tau + \alpha
$

and take logs of the data in the table, and we have a bog standard linear regression problem.

RonL