Find the equation of the exponential function represented by the table below:xx yy00 0, point, 10.111 0, point, 30.322 0, point, 90.933 2, point, 72.7
Question
Find the equation of the exponential function represented by the table below:xx yy00 0, point, 10.111 0, point, 30.322 0, point, 90.933 2, point, 72.7
Solution
The general form of an exponential function is y = ab^x.
From the table, we can see that when x = 0, y = 0.1. This gives us the equation 0.1 = ab^0. Since any number (except 0) to the power of 0 is 1, we can simplify this to 0.1 = a.
So, we now know that a = 0.1.
Next, we need to find the value of b. We can use another point from the table to do this. Let's use the point (1, 0.3). Substituting these values into the equation gives us 0.3 = 0.1b^1. Simplifying this gives us b = 0.3 / 0.1 = 3.
So, the equation of the exponential function represented by the table is y = 0.1 * 3^x.
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