Using Graph to determine constants in equation

In summary, the equation F= x + kx^n is being used to determine the constants k and n. The correct way to do this is to plot log(F-x) in terms of logx, where the y-intercept represents logk and the slope represents n. This method will help find the correct values for k and n.
  • #1
yardy_genius
13
0
Hello,

i have the equation F= x + kx^n

I am trying to determine the constants k and n? where i have the ranges for F and x

is what i am doing correct?

log F= logx + logk+ nlogx

log F= logx(1+n) + logk


ok i would then plot logF vs Log x. if i am correct logk = y intercept and from that k can be calculated. How would i use the gradient to find the value of n. can someone please give me some assistance. much appreciated.
 
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  • #2
yardy_genius said:
Hello,

i have the equation F= x + kx^n

I am trying to determine the constants k and n? where i have the ranges for F and x

is what i am doing correct?

log F= logx + logk+ nlogx
No, it is WRONG... log(a+b) is not equal to log(a )+ log(b)

But log(F-x)=log(kx^n)= logk+n logx.

Plot out log(F-x) in terms of logx. It has to be a straight line, with y-intercept logk and slope n.

ehild
 
Last edited:
  • #3
ehild said:
No, it is WRONG... log(a+b) is not equal to log(a )+ log(b)

But log(F-x)=log(kx^n)= logk+n logx.

Plot out log(F-x) in terms of logx. It has to be a straight line, with y-intercept logk and slope n.

ehild

thank you very much for that correction!
 

Related to Using Graph to determine constants in equation

1. How do I use a graph to determine the constants in an equation?

To use a graph to determine the constants in an equation, you first need to plot the data points on the graph. Then, you can use the slope of the line to determine the value of one of the constants. Next, you can use one of the data points to solve for the other constant using the equation. Finally, you can use both constants to create the equation for the line on the graph.

2. What is the importance of using a graph to determine constants in an equation?

Using a graph to determine constants in an equation allows you to visually see the relationship between the variables. It also provides a more accurate way to determine the constants, as you are able to use multiple data points and see the overall trend of the data.

3. Can a graph be used to determine constants in any type of equation?

Yes, a graph can be used to determine constants in any type of equation as long as there is a relationship between the variables. This includes linear, quadratic, exponential, and logarithmic equations.

4. Is the process of using a graph to determine constants in an equation always accurate?

No, the accuracy of using a graph to determine constants in an equation depends on the quality and reliability of the data points. If the data points are not accurately measured or there is a lot of variation in the data, the constants may not be determined accurately.

5. Are there any limitations to using a graph to determine constants in an equation?

One limitation of using a graph to determine constants in an equation is that it may not work for non-linear relationships between variables. In addition, if there are significant outliers in the data, they may skew the results and make it difficult to accurately determine the constants.

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