Find the equation of the exponential function represented by the table below:
x y
0 1
1 2
2 4
3 8
The exponential function represented by the table is of the form y = a * b^x, where a is the initial value and b is the constant ratio.
Given the table:
x y
0 1
1 2
2 4
3 8
Let's find the value of b. Since the ratio of consecutive y-values is constant, we can divide any y-value by the previous y-value to find the value of b.
b = 2/1 = 4/2 = 8/4 = 2
Now, let's find the value of a by substituting x=0 and y=1 into the equation:
1 = a * 2^0
1 = a * 1
a = 1
Therefore, the equation of the exponential function represented by the table is:
y = 1 * 2^x