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 y=abxy = ab^x for the given data, we'll follow the same steps as before:

  1. Transform the data: Convert the yy values to their logarithms so the equation becomes linear.
  2. Apply linear regression: Perform linear regression on log(y)\log(y) versus xx to find the slope and intercept.
  3. Determine aa and bb: Calculate the values of aa and bb from the slope and intercept.

Let me calculate this now.The exponential equation that best fits the new data is:

y=734.03×(1.584)xy = 734.03 \times (1.584)^x

Where a734.03a \approx 734.03 and b1.584b \approx 1.584.

Would you like any further details or have any questions about this calculation? Here are some related questions you might find useful:

  1. How does changing the dataset affect the values of aa and bb in the exponential equation?
  2. What is the significance of the base bb in an exponential growth model?
  3. How can you interpret the slope of the linearized regression in terms of the original exponential model?
  4. What are some real-world examples where exponential regression might be useful?
  5. How can you determine the goodness of fit for this exponential model?

Tip: When comparing different exponential models, the value of bb 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