Find the equation of the exponential function represented by the table below:xx yy00 0, point, 0, 20.0211 0, point, 0, 10.0122 0, point, 0, 0, 50.00533 0, point, 0, 0, 2, 50.0025
Question
Find the equation of the exponential function represented by the table below:xx yy00 0, point, 0, 20.0211 0, point, 0, 10.0122 0, point, 0, 0, 50.00533 0, point, 0, 0, 2, 50.0025
Solution
The general form of an exponential function is y = ab^x.
From the table, we can see that when x = 0, y = 0.02. This gives us the y-intercept and tells us that a = 0.02.
Next, we need to find the base (b). We can do this by taking two points from the table and setting up the equation:
0.01 = 0.02 * b^1 0.01/0.02 = b 0.5 = b
So, the equation of the exponential function represented by the table is y = 0.02 * 0.5^x.
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