Find the equation of the exponential function represented by the table below:
xx yy
00 0, point, 0, 10.01
11 0, point, 0, 0, 50.005
22 0, point, 0, 0, 2, 50.0025
33 0, point, 0, 0, 1, 2, 50.00125
To find the equation of the exponential function represented by the given table, we can observe that the y-values are decreasing as the x-values increase. This indicates that the exponential function has a base less than 1.
Let's denote the base of the exponential function as b. Then, the equation for the exponential function can be written as:
y = a * b^x
where a is the initial value of y when x = 0, and x is the independent variable.
Using the given values from the table, we can find the value of b.
When x = 0, y = 10.01, so we have:
10.01 = a * b^0
10.01 = a
When x = 1, y = 0.50.005, so we have:
0.50.005 = 10.01 * b^1
0.50.005 = 10.01 * b
b ≈ 0.500
So the equation for the exponential function represented by the table is:
y = 10.01 * (0.500)^x