Answer:
[tex]y=4(3)^x[/tex]
Step-by-step explanation:
From the table given in the question,
x y Difference Ratio
1 12 - -
2 36 36-12 = 24 [tex]\frac{36}{12}=3[/tex]
3 108 108-36 = 72 [tex]\frac{108}{36}=3[/tex]
4 324 324-108 = 216 [tex]\frac{324}{108}=3[/tex]
5 972 972-324 = 648 [tex]\frac{648}{216}=3[/tex]
There is a common ratio of 3 in each successive term.
Therefore, data given in the table will represent an exponential function.
[tex]y=a(b)^x[/tex]
For a point [tex](1, 12),[/tex]
[tex]12=a(b)^1[/tex]
[tex]ab=12[/tex] ------(1)
For another point of the table [tex](2,36)[/tex],
[tex]36=a(b)^2[/tex]
[tex]ab^2=36[/tex] --------(2)
Equation (2) divided by equation (1)
[tex]\frac{ab^2}{ab}=\frac{36}{12}[/tex]
[tex]b=3[/tex]
From equation (1),
[tex]3a=12[/tex]
[tex]a=4[/tex]
Therefore, exponential function will be,
[tex]y=4(3)^x[/tex]
