Math Problem Statement

Exponential Regression In Exercises S-12 through S-14, use exponential regression to fit the data set. Give the exponential model, and plot the data along with the model.

x 4 11 15 17 18 Generate a graph on the exponential regression as y=0.20 times (1.50)^x

Solution

Here is the plot of the exponential regression model y=0.20×(1.50)xy = 0.20 \times (1.50)^x along with the given data points. The red dots represent the data points, and the blue curve represents the exponential model.

Would you like further details or have any questions about the calculations or the plot?

Here are 5 related questions to deepen your understanding:

  1. How does changing the base of the exponential function 1.501.50 affect the curve?
  2. What is the significance of the constant 0.20 in the exponential equation?
  3. How can you calculate the rate of growth from the exponential model?
  4. How would the graph change if the data points were more widely spaced on the xx-axis?
  5. How can exponential regression be used to model real-life phenomena like population growth?

Tip: When interpreting exponential models, the base of the exponent (here 1.501.50) indicates how quickly the function grows or decays as xx increases.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Regression Analysis
Curve Fitting

Formulas

Exponential Model: y = a * (b)^x

Theorems

Exponential Growth Theorem

Suitable Grade Level

Grades 10-12