Answer:
The correct option is C.
Step-by-step explanation:
The required formulas are:
1. [tex]\overline{x}=\frac{\sum{x}}{n}[/tex]
2. [tex]\overline{\ln y}=\frac{\sum{\ln y}}{n}[/tex]
3. Tread line is
[tex]y=AB^x[/tex]
Where, [tex]B=e^{\frac{S_{xy}}{S_{xx}}}[/tex] and [tex]A=e^{\overline{\ln y}-\overline{x}\ln B}[/tex]
4. [tex]S_{xx}=\frac{\sum({x-\overline{x}})^2}{n}[/tex]
5. [tex]S_{xy}=\frac{\sum({x-\overline{x}})(\ln y-\overline{\ln y})}{n}[/tex]
The values of x and y are
x : 0 1 2 3 4 5 6
y : 10.5 7.8 6.3 5.1 4.4 3.6 3.1
Using the above formulas,
mean of x=3
mean of [tex]y=5.372635247[/tex]
[tex]A=9.75319281[/tex]
[tex]B=0.819747654[/tex]
Therefore the exponential regression equation of the line is
[tex]y=9.75(0.8197)^x[/tex]
Therefore option C is correct.
