Find the equation of the exponential function represented by the table below:
x y
0, 0.01
1, 0.04
2, 0.16
3, 0.64
To find the equation of an exponential function, we need to determine the growth factor and the base.
From the table, we observe that each y-value is the previous y-value multiplied by a constant factor of 4:
0.04 / 0.01 = 4
0.16 / 0.04 = 4
0.64 / 0.16 = 4
Thus, the growth factor is 4.
The base can be found by dividing any y-value by the corresponding x-value. Let's use the first data point:
y / x = 0.01 / 0 = undefined
Since we cannot divide by 0, we can conclude that the base is not 0.
Therefore, the equation of the exponential function is:
y = ab^x
where b is the base and a is the initial value of y.
In this case, we know that the growth factor is 4, so the base, b, is 4.
Using the first data point (0, 0.01), we can find the value of a:
0.01 = a * 4^0
0.01 = a * 1
a = 0.01
Thus, the equation of the exponential function represented by the table is:
y = 0.01 * 4^x