Given:
The points lie on the graph are (1,1) and (2,3).
Required:
We need to find the equation of the given graph.
Explanation:
Consider the individual equation.
A.
[tex]y=1.5^{(x+2)}-3[/tex]
Substitute x =1 and y =1 in the equation.
[tex]1=1.5^{(1+2)}-3[/tex][tex]1=0.375[/tex]
This is not true,
This is not a required equation.
B.
[tex]y=2^x+6[/tex]
Substitute x =1 and y =1 in the equation.
[tex]1=2^1+6[/tex][tex]1=8[/tex]
This is not true,
This is not a required equation.
C.
[tex]y=(\frac{1}{2})^x+6[/tex]
Substitute x =1 and y =1 in the equation.
[tex]1=(\frac{1}{2})^1+6[/tex][tex]1=6.5[/tex]
This is not true,
This is not a required equation.
D.
[tex]y=3^{(x-1)}[/tex]
Substitute x =1 and y =1 in the equation.
[tex]1=3^{(1-1)}[/tex][tex]1=1[/tex]
This is true.
Substitute x =2 and y =3 in the equation.
[tex]3=3^{(2-1)}[/tex][tex]3=3[/tex]
This is true.
This is a required equation.
Final answer:
[tex]y=3^{(x-1)}[/tex]
