Hope this helps
The general form of an exponential function is y = a(b)^x, where 'a' is the initial value or y-intercept, 'b' is the growth factor or base, and 'x' is the input variable.
To find the equation of the exponential function represented by the table, we need to determine the values of 'a' and 'b'.
From the table, we can see that when x = 0, y = 3. This means that the initial value or y-intercept is 3, so we can set a = 3.
Next, we can use the values of y to find the growth factor or base 'b'. We can start by finding the ratio of two consecutive y-values:
12/3 = 4
48/12 = 4
192/48 = 4
The ratio of any two consecutive y-values is constant and equal to the growth factor 'b'. Therefore, we can set b = 4.
Now we can write the equation of the exponential function:
y = 3(4)^x
Therefore, the equation of the exponential function represented by the table is y = 3(4)^x.