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

Question

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

Answer 1

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