To find the exponential regression model for the given data set:
| \( x \) | \( y \) |
|---|---|
| 2 | 1 |
| 3 | 2.5 |
| 4 | 4.4 |
| 5 | 7.5 |
| 6 | 12.1 |
| 7 | 18.2 |
We need to determine the values of the parameters \( a \) and \( b \) in the exponential model of the form:
[tex]\[ y = a \cdot b^x \][/tex]
Through the process of finding the best fit, we get that:
[tex]\[
a \approx 0.4 \quad \text{and} \quad b \approx 1.76
\][/tex]
Thus, the exponential regression model that best fits the given data set is:
[tex]\[ y = 0.4 \cdot (1.76)^x \][/tex]
Therefore, the correct answer is:
[tex]\[ y = 0.4(1.76)^x \][/tex]
