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Find the equation of the exponential function represented by the table below:xx yy00 1111 3322 9933 2727

Question

Find the equation of the exponential function represented by the table below:xx yy00 1111 3322 9933 2727

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Solution

The table represents an exponential function of the form y = ab^x.

Here are the steps to find the equation:

  1. Identify two points from the table. Let's use (0, 1) and (1, 3).

  2. Substitute these points into the equation y = ab^x to create two equations.

    For (0, 1), we get 1 = ab^0, which simplifies to 1 = a, since anything raised to the power of 0 is 1.

    For (1, 3), we get 3 = ab^1, which simplifies to 3 = a*b, since anything raised to the power of 1 is itself.

  3. Substitute a = 1 into the second equation to solve for b. We get 3 = 1*b, which simplifies to b = 3.

  4. Substitute a = 1 and b = 3 back into the equation y = ab^x to get the final equation, which is y = 1*3^x, or y = 3^x.

So, the equation of the exponential function represented by the table is y = 3^x.

This problem has been solved

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