Math Problem Statement
x
1
2
3
4
5
6
y
1181
1773
3065
4381
7578
11513
Use regression to find an exponential equation that best fits the data above. The equation has form y=ab upperindex x where:
Solution
To find the best-fitting exponential equation of the form for the given data, we'll follow the same steps as before:
- Transform the data: Convert the values to their logarithms so the equation becomes linear.
- Apply linear regression: Perform linear regression on versus to find the slope and intercept.
- Determine and : Calculate the values of and from the slope and intercept.
Let me calculate this now.The exponential equation that best fits the new data is:
Where and .
Would you like any further details or have any questions about this calculation? Here are some related questions you might find useful:
- How does changing the dataset affect the values of and in the exponential equation?
- What is the significance of the base in an exponential growth model?
- How can you interpret the slope of the linearized regression in terms of the original exponential model?
- What are some real-world examples where exponential regression might be useful?
- How can you determine the goodness of fit for this exponential model?
Tip: When comparing different exponential models, the value of gives you a quick sense of how rapidly the dependent variable is increasing or decreasing.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Logarithms
Linear Regression
Formulas
Exponential growth equation y = ab^x
Theorems
-
Suitable Grade Level
Advanced High School
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