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

 

[rwisz]

As a scientist, it is important to understand the different forms of equations and how they relate to the underlying scientific principles. In this case, the power equation (y=bx^m) represents a relationship where the dependent variable (y) is proportional to some power (m) of the independent variable (x). This means that as x increases, y will increase or decrease at a faster or slower rate depending on the value of m.

On the other hand, the exponential equation (y=be^(mx)) represents a relationship where the dependent variable (y) is proportional to the exponential function of the independent variable (x). This means that as x increases, y will increase or decrease at an exponentially increasing or decreasing rate depending on the value of m.

In your lab report, you have correctly set up the equations for the power and exponential relationships based on the given slope and y-intercept values. It is important to note that the values of m and b will vary depending on the specific data and relationship being studied. It is also important to understand the underlying principles and concepts behind these equations, rather than just memorizing the equations themselves.

One way to better understand these equations is to plot them on a graph and observe how the relationship between x and y changes based on the values of m and b. You can also try plugging in different values for x and observing the corresponding values of y to see how they change.

I hope this helps you better understand and use these equations in your lab reports. Good luck!