How to workout the exponential curve using x and y values and without excel

In summary: P.S. If the y value for the x = 107.61 data point is correct, then Excel's exponential fit is about 3 times better than the linear fit (r^2 ~ 0.5 vs. r^2 ~ 0.17). Still not very good.
  • #1
masterims
4
0
Hi All,

I have searched for hours but cannot figure this out. I need to find the equation for an exponential curve but I only have the x and y values. Is there a way to do this without using excel?

I tried to follow this on YouTube: https://www.youtube.com/watch?v=ta4MZS7w2VA but the equation I got for the data below was different to what excel produces.

x......y
78.46......99.572
90.12......99.56
107.61......99.545
101.78......99.531
119.27......99.514
101.78......99.5
113.44......99.484
107.61......9.469

Thank you,
Imran
 
Mathematics news on Phys.org
  • #2
masterims said:
Hi All,

I have searched for hours but cannot figure this out. I need to find the equation for an exponential curve but I only have the x and y values. Is there a way to do this without using excel?

I tried to follow this on YouTube: https://www.youtube.com/watch?v=ta4MZS7w2VA but the equation I got for the data below was different to what excel produces.

x......y
78.46......99.572
90.12......99.56
107.61......99.545
101.78......99.531
119.27......99.514
101.78......99.5
113.44......99.484
107.61......9.469

Thank you,
Imran

Hi masterims! Welcome to MHB! :)

Yes, there are other ways than to use Excel.
Actually, you can use Excel in other ways to find an exponential equation.

But before we go there, let's start with your data points.
From visual inspection, I can see that your x-data is distributed with a reasonable range.
However, your y-data is nearly constant (with 1 exception).
So it doesn't seem to match an exponential curve at all.

Moreover, you have a far outlier in your last data point.
Whatever you do, this will have a disastrous effect on any exponential curve match.
 
  • #3
masterims said:
Hi All,

I have searched for hours but cannot figure this out. I need to find the equation for an exponential curve but I only have the x and y values. Is there a way to do this without using excel?

I tried to follow this on YouTube: https://www.youtube.com/watch?v=ta4MZS7w2VA but the equation I got for the data below was different to what excel produces.

x......y
78.46......99.572
90.12......99.56
107.61......99.545
101.78......99.531
119.27......99.514
101.78......99.5
113.44......99.484
107.61......9.469

Thank you,
Imran
I'm going to assume that the y value for the x = 107.61 data point is a typo (y = 99.459?), not an outlier. However the exponential fit and the linear fit to the data are both horrible: I get r^2 = 0.5 (or so) for both fits. So it doesn't matter what method you use...I can't think of a way to do it without Excel, unless you wish to do some time consuming calculator work. But seeing as you are going to get lousy results, I'd say talk to your instructor first.

-Dan
 

FAQ: How to workout the exponential curve using x and y values and without excel

How do I calculate the exponential curve using x and y values?

To calculate the exponential curve using x and y values, you can use the formula y = ab^x, where a is the initial value and b is the growth factor. Simply plug in your x and y values into this formula and solve for a and b. Alternatively, you can use logarithms to convert the exponential equation into a linear one and then use linear regression to find the values of a and b.

Can I workout the exponential curve without using Excel?

Yes, you can calculate the exponential curve without using Excel. As mentioned before, you can use the formula y = ab^x or use logarithms to convert the equation into a linear one. There are also online calculators and software programs available that can help you calculate the exponential curve.

What is the difference between linear and exponential growth?

Linear growth refers to a constant increase where the value of y changes by the same amount for each unit change in x. Exponential growth, on the other hand, refers to a constant percentage increase where the value of y changes by a fixed percentage for each unit change in x. This means that exponential growth increases at a faster rate than linear growth.

How do I interpret the values of a and b in the exponential curve equation?

The value of a represents the initial value or starting point of the exponential curve, while the value of b represents the growth factor or rate at which the curve increases. For example, if a = 2 and b = 1.5, the equation would be y = 2(1.5)^x. This means that the initial value is 2 and the curve will increase by 50% for each unit change in x.

Can the exponential curve be used to predict future values?

Yes, the exponential curve can be used to predict future values based on the trend shown by the given x and y values. However, it is important to note that the accuracy of the predictions will depend on the quality and quantity of the data used to create the curve. It is always recommended to use caution when making predictions and to regularly update the curve with new data as it becomes available.

Hot Threads

Recent Insights

Back
Top