Given:
Given that the values of x and y in the table.
We need to determine the equation for the exponential function represented in the table and graph the equation.
Equation for the exponential function:
The general equation for the exponential function is given by
[tex]y=a(b)^x[/tex] ------- (1)
Substituting the coordinate (0,6) in equation (1), we get;
[tex]6=a(b)^0[/tex]
[tex]6=a[/tex]
Thus, the value of a is 6.
Substituting a = 6 in equation (1), we have;
[tex]y=6(b)^x[/tex] -------- (2)
Substituting the coordinate (1,12) in equation (2), we get;
[tex]12=6(b)^1[/tex]
[tex]12=6b[/tex]
[tex]2=b[/tex]
Thus, the value of b is 2.
Substituting b = 2 in equation (2), we get;
[tex]y=6(2)^x[/tex]
Thus, the equation for the exponential function is [tex]y=6(2)^x[/tex]
The image of the graph of the exponential function is attached below:
