Find the equation of the exponential function represented by the table below:xx yy00 0, point, 0, 10.0111 0, point, 0, 30.0322 0, point, 0, 90.0933 0, point, 2, 70.27
Question
Find the equation of the exponential function represented by the table below:xx yy00 0, point, 0, 10.0111 0, point, 0, 30.0322 0, point, 0, 90.0933 0, point, 2, 70.27
Solution
The table seems to represent an exponential function of the form y = ab^x.
To find the values of a and b, we can use two points from the table. Let's use the points (0, 0.01) and (1, 0.03).
First, we can plug the first point into the equation:
0.01 = a * b^0
Since any number to the power of 0 is 1, we find that a = 0.01.
Next, we can plug the second point and the value of a into the equation:
0.03 = 0.01 * b^1
Solving for b, we get b = 0.03 / 0.01 = 3.
So, the equation of the exponential function represented by the table is y = 0.01 * 3^x.
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