Find the equation of the exponential function represented by the table below:

Question

x y
0 1
1 0.5
2 0.25
3 0.125

Answer 1

The general form of an exponential function is given by:

y = ab^x

To find the equation of the exponential function represented by the table, we need to find the values of a and b.

Using the given values from the table, we can substitute them into the equation to form a system of equations:

For the first point (x=0, y=1):
1 = ab^0
Since any number raised to the power of 0 is 1, we can simplify this to:
1 = a

For the second point (x=1, y=0.5):
0.5 = a * b^1
Since we know a=1, we can substitute this into the equation and simplify it further:
0.5 = 1 * b
0.5 = b

Therefore, the value of a is 1 and the value of b is 0.5.

So, the equation of the exponential function represented by the table is:
y = 1 * (0.5)^x
Or, simplifying it further:
y = (0.5)^x