course mth 163
9-22-09 10:30 pm*********************************************
Question: explain the steps in fitting an exponential function to data
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Your solution:
You can substitute the data into the exponential function. For example, if you were given x and y values and asked to match them to exponential functions, you could put the x value in and see if you get the correct y solution, and if you did, it would be the right match. If the data you were given happens to be graphs and you are asked to match the functions to the graph, you could make a table of values to insert into the functions to see which graph belongs with which function.
confidence rating: 2
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Given Solution:
`a** If you have two points you can solve the simultaneous equations. If you have a more extensive data set you use
transformations.
For exponential data you plot log(y) vs. x. If the graph is a straight line then you have a good fit.
If the slope is m and the vertical intercept is b then your graph gives you log(y) = m x + b.
You invert the transformation using the inverse function 10^x, obtaining 10^log(y) = 10^(mx+b) so that
y = 10^(mx) * 10^b, and then rearrange this into the desired form.
Note that if a power function fits the data then log y vs. log x will give a straight line so that log y = m log x + b. In this
case our solution will be y = 10^b * x^m, a power function rather than an exponential function. **
You did not address the use of the log functions or the general procedures for linearizing data.
I recommend that you insert a detailed self-critique, showing me what you do and do not understand about the details of the given solution, and resubmit.