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Given the following data set, find an exponential regression model.

\begin{tabular}{|l|l|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
2 & 1 \\
\hline
3 & 2.5 \\
\hline
4 & 4.4 \\
\hline
5 & 7.5 \\
\hline
6 & 12.1 \\
\hline
7 & 18.2 \\
\hline
\end{tabular}

A. [tex]$y=1.76(0.4)^x$[/tex]

B. [tex]$y=0.4(1.76)^x$[/tex]

C. [tex]$y=0.4+(1.76)x$[/tex]

D. [tex]$y=1.76+(0.4)x$[/tex]

Sagot :

GinnyAnswer
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]
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