Power and Exponential Equations

[beanus]

Homework Statement

I'm writing a lab report and I'm having trouble understanding how to set up these experimental equations.

I understand Linear (y=mx+b) but my professor wants us to use separate equations to illustrate power and exponential forms.
Power : y=bx^m
Exponential: y=be^(mx)

On the first lab report for the power relationship I had:
Slope of linearization equation (trendline) = 4
Y intercept of linearization equation = .9031
I set up my equation as y=.9031x^4

For the exponential relationship I had:
Slope of linearization equation (trendling) = 1.3029
Y intercept of linearization equation (trendline) = .699
I set up my equation as y=.699e^(1.3029x)

Does anyone know how to use these equations?

Homework Equations

Power : y=bx^m
Exponential: y=be^(mx)

The Attempt at a Solution

y=.9031x^4
y=.699e^(1.3029x)


Thanks!

 

[ojs]

Hmm, I am sorry, I don't understand your work here.

Are you using data sets that show linear relationship, making a linear fit to them and using the parameters from that fit to put into a power and exponential equation? That won't work at all.

If you have data sets that show either power or exponential relations then you either use a program to fit that data to the given equation or take the n-th root or logarithm of the y-data and then use linear fitting.

And what do you mean by "how to use these equations"?

 

[Ray Vickson]

Homework Statement

I'm writing a lab report and I'm having trouble understanding how to set up these experimental equations.

I understand Linear (y=mx+b) but my professor wants us to use separate equations to illustrate power and exponential forms.
Power : y=bx^m
Exponential: y=be^(mx)

On the first lab report for the power relationship I had:
Slope of linearization equation (trendline) = 4
Y intercept of linearization equation = .9031
I set up my equation as y=.9031x^4

For the exponential relationship I had:
Slope of linearization equation (trendling) = 1.3029
Y intercept of linearization equation (trendline) = .699
I set up my equation as y=.699e^(1.3029x)

Does anyone know how to use these equations?

Homework Equations

Power : y=bx^m
Exponential: y=be^(mx)

The Attempt at a Solution

y=.9031x^4
y=.699e^(1.3029x)


Thanks!

The claim in your first lab report looks wrong. If you say "slope of trendline = 4" (after your word "linearization") you are claiming an equation of the form y = a + 4*x---that is what we mean when we say a linear function with trendline having slope 4. However, if you were looking at *log(y)* vs. *log(x)* and getting a linear form with trendline = 4 (that is, log(y) = c + 4*log(x)), _then_ you would, indeed, have y = a*x^4.

RGV

 

[beanus]

Thanks I think I got it