Certainly! Let's derive the best fit exponential function [tex]\( y = a b^x \)[/tex] from the given data:
The data points provided are:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
0 & -0.7 \\
1 & -1.06 \\
2 & -1.62 \\
3 & -2.46 \\
4 & -3.74 \\
5 & -5.68 \\
\end{array}
\][/tex]
To find the best fit exponential function [tex]\( y = a b^x \)[/tex], we perform exponential regression, which allows us to fit a curve of the form [tex]\( y = a b^x \)[/tex] to the data points. After carrying out the exponential regression process, we determine the parameters [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
The calculated parameters (rounded to two decimal places) are:
[tex]\[
a = -0.70
\][/tex]
[tex]\[
b = 1.52
\][/tex]
Therefore, the best fit exponential function for the given data is:
[tex]\[
y = -0.70 \cdot 1.52^x
\][/tex]
So, the equation of the curve that best fits the given data points is:
[tex]\[
y = -0.70 \cdot 1.52^x
\][/tex]
