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Find the equation of the exponential function represented by the table below:xx yy00 3311 1, point, 51.522 0, point, 7, 50.7533 0, point, 3, 7, 50.375

Question

Find the equation of the exponential function represented by the table below:xx yy00 3311 1, point, 51.522 0, point, 7, 50.7533 0, point, 3, 7, 50.375

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Solution

The general form of an exponential function is y = ab^x.

To find the equation of the exponential function represented by the table, we need to find the values of a and b.

Step 1: Find the value of a The value of a is the y-intercept, which is the value of y when x = 0. From the table, when x = 0, y = 3.33. So, a = 3.33.

Step 2: Find the value of b To find the value of b, we can use any other point from the table. Let's use the point (1, 1.51). Substitute x = 1, y = 1.51, and a = 3.33 into the equation y = ab^x:

1.51 = 3.33 * b^1 => b = 1.51 / 3.33 => b = 0.453

So, the equation of the exponential function represented by the table is y = 3.33 * (0.453)^x.

This problem has been solved

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