Linear law to Non-Linear Functions

[stevemustaine]

Hello everyone

Need some help on this question:

Following data is obtained from an experiment, xy & y are related by y = ab^x

The values are

x	1	2	3	4
y	28	200	1590	7950

a) Explain how a straight line may be plotted. Answer given in the book is log y=(log b)x + log 9
My answer is:
log y = log a + xlog b
log y = (logb)x + log a

b) Plot the graph of straight line & draw the line of best fit
c) Use the line obtained to find the value of a & b . Ans is 5.012, b=11.5

Please advice on a & b, all help appreciated.

Thank you.

 

[Ishuda]

Hello everyone

Need some help on this question:

Following data is obtained from an experiment, xy & y are related by y = ab^x

The values are

x	1	2	3	4
y	28	200	1590	7950

a) Explain how a straight line may be plotted. Answer given in the book is log y=(log b)x + log 9
My answer is:
log y = log a + xlog b
log y = (logb)x + log a

b) Plot the graph of straight line & draw the line of best fit
c) Use the line obtained to find the value of a & b . Ans is 5.012, b=11.5

Please advice on a & b, all help appreciated.

Thank you.

You've posted this problem under the sub-forum Arithmetic and I don't see a solution under that heading. So what have you been studying recently [possibly anything about least squares fit?] and how might that apply? You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

As a hint you might let
c = ln(b),
d = ln(a),
and
u = ln(y)
where ln is the natural logarithm. Your table then becomes (to two decimal places)

x	1	2	3	4
u	3.33	5.30	7.37	8.99

and the equation becomes
u = c x + d

 

[stevemustaine]

Thank you for your reply, but i found the answer already. Your answer in incorrect, but anyway, thank you.