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

The y-values in the table are decreasing, which suggests that the base (b) is between 0 and 1.

From the table, when x = 0, y = 5.5. This gives us the y-intercept and tells us that a = 5.5.

Next, we need to find the base (b). We can use the points (1, 2.75) and (2, 1.375) for this.

The exponential function formula is y = ab^x. We can plug in the values from one of the points and solve for b.

Using the point (1, 2.75), we get:

2.75 = 5.5 * b^1
b = 2.75 / 5.5
b = 0.5

So, the equation of the exponential function represented by the table is y = 5.5 * 0.5^x.

Question

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

The y-values in the table are decreasing, which suggests that the base (b) is between 0 and 1.

From the table, when x = 0, y = 5.5. This gives us the y-intercept and tells us that a = 5.5.

Next, we need to find the base (b). We can use the points (1, 2.75) and (2, 1.375) for this.

The exponential function formula is y = ab^x. We can plug in the values from one of the points and solve for b.

Using the point (1, 2.75), we get:

2.75 = 5.5 * b^1
b = 2.75 / 5.5
b = 0.5

So, the equation of the exponential function represented by the table is y = 5.5 * 0.5^x.

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