How can algebra be used to convert an exponential graph into a linear graph?

[ishaquea]

URGENT: Basic graphing question

I have the equation y=1.234x^(-0.567). First part of the question was the plot a graph for it from points 0.01, 0.1, 1, 10, 100... 10000. I got that part (on excel) It's an exponential graph.

Second part says, and here's where I am confused, plot Y=y and X=x^(-0.567) from the same x values. My understanding is that the Y values will stay the same, and the X values will be different based on the new X formula.

The question asks whether the graph will be a straight line. I said no based on excel and intuition because X is still changing exponentially. However, the next question says the following:

"This problem shows two main methods that are widely used to manipulate a mathematical formula (model) to convert and then analyze it in the standard form of a straight line". How does that method convert it to straight line? It's still an exponential relation, isn't it? Another classmate of mine got a straight, but I don't know how. How do you convert an exponential graph into a linear graph without using logs with just algebra?

Please help!

 

[Vorde]

Well first of all, y=1.234^(-0.567) isn't an exponential graph, it's a straight any. Any equation that has no variables will come out with a flat line (a.k.a. its a constant value regardless of x, because x isn't in the equation).

See if that makes sense now.

 

[ishaquea]

Ah, stupid me. I wrote the equation wrong. Sorry! it's supposed to be y = 1.234 x^(-0.567)

 

[Vorde]

Sorry I'm not quite sure how to help, however what I can say with almost definite certainty is that there is no way to change what a graph looks like without modifying the equation (and changing the axis', but that doesn't really count).

EDIT: Where I'm stuck is when you said

plot Y=y and X=x^(-0.567) from the same x values.

I'm not quite sure what is meant by splitting up the graph like that.

 

[ishaquea]

okay my question was this:

plot on the X-axis: X=x^-0.567, where x = 0.01, 0.1, 1... 100, 1000, etc

plot on the Y-axis: Y=y, where y=1.234x^-0.567

My problem is that, apparently, doing that will convert the original exponential equation (y = 1.234x^-0.567) to a straight line. But I can't get it to be a straight line in MS EXCEL when I plot using the x-values.

Prof said that the above way and using logs are two ways to analyze an equation in their linear form. I don't get how you can convert an exponential equation into a linear graph without using logs.

Thanks for trying to help still!

 

[ishaquea]

PS. I attached the assignment file. It's question 1.1 that I'm having trouble with.

 

[Vorde]

Ah, I see what's going on. I'm can't help with the logistics of graphing it, but I can explain what's going on.

Normally when you graph a function you partition a given view of the y and x axis' into an equal number of parts, each which represent the same value (for instance in a graph one notch up on the y-axis and one notch to the right on the x-axis both equal the same numerical value; 1). So when you graph a straight line, for a given change in x you have a set change in y, valid for any x value. When you graph a non straight line, for a given value of x, the y value can be anything depending on the equation, so if you move one notch over on the x axis, you might move up more or less than one notch on the y axis.

One way of fixing this, is to define a set change in the x notches (by saying x=x on the axis), and making it so the notches on the y-axis are based on the equation. So if the equation triples in value over a x increase of 1 notch, the y notches become 3 times bigger, and so on. When you think about that in your head, you'll realize that the graph you'll get when you base the change in y-notches off the equation will be a straight line.

Tell me if you need some more clarifying, I didn't do a great job.

 

[ishaquea]

i sort of see what you're saying... but how do i do graph it in straight line on excel...? :(

 

[Integral]

Put your given x values in column A in cell B1 compute A1^.567 now copy that down col b for all x values. In col c compute your given function y.

Now plot A vs C and B vs C. The second plat will be a straight line.