If your solution to stated problem does not match the given solution, you should self-critique per instructions at

 

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

 

 

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

 

019. `query 19

Question: `qexplain the steps in fitting an exponential function to data

 

Your solution:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

Given Solution:

`a** If you have two points you can solve the simultaneous equations:

• Substitute the coordinates into the form y = A b^x and solve the two resulting equations for A and b. 

• You could alternatively use the form y = A * 2^(k x) or y = A * e^(k x), in which case you would solve for A and k.

 

If you have a more extensive data set you can use transformations.

 

For exponential data you plot log(y) vs. x. If the graph is well approximated by a straight line then you get an exponential function.

 

Then since the graph is a straight line, you can find its equation using using either slope and vertical intercept, or two points on the line.

 

If the slope of a y vs. x graph is m and the vertical intercept is b then the function is y = m x + b. 

 

However in this case the graph is not of y vs. x, but of log(y) vs. x. 

 

So if the slope of your graph is m and the y intercept is b, the function is log(y) = m x + b.

 

This equation needs to be solved for y:

You invert the transformation using the inverse function 10^x, obtaining 10^log(y) = 10^(mx+b).

 

10^log(y) = y, by the definition of the logarithm, and

10^(mx + b) = 10^(mx) * 10^b, by the laws of exponents.

 

Thus

• y = 10^(mx) * 10^b,

where m and b are just the numbers (slope and vertical intercept) that you determined from your graph.

 

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. **

 

 

 

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique rating:

 

If you understand the assignment and were able to solve the previously given problems from your worksheets, you should be able to complete most of the following problems quickly and easily.  If you experience difficulty with some of these problems, you will be given notes and we will work to resolve difficulties.