To determine the correct exponential equation based on the points and the behavior of the curve, we will evaluate the given options with respect to the points (1, 14) and (2, 4) that lie on the curve.
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Option #1: \( y = 7(12)^x \)
- For \( x = 1 \): \( y = 7(12)^1 = 7 \times 12 = 84 \) (not correct)
- For \( x = 2 \): \( y = 7(12)^2 = 7 \times 144 = 1008 \) (not correct)
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Option #2: \( y = 49(27)^x \)
- For \( x = 1 \): \( y = 49(27)^1 = 49 \times 27 = 1323 \) (not correct)
- For \( x = 2 \): \( y = 49(27)^2 = 49 \times 729 = 35721 \) (not correct)
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Option #3: \( y = 7(27)^x \)
- For \( x = 1 \): \( y = 7(27)^1 = 7 \times 27 = 189 \) (not correct)
- For \( x = 2 \): \( y = 7(27)^2 = 7 \times 729 = 5103 \) (not correct)
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Option #4: \( y = 49(72)^x \)
- For \( x = 1 \): \( y = 49(72)^1 = 49 \times 72 = 3528 \) (not correct)
- For \( x = 2 \): \( y = 49(72)^2 = 49 \times 5184 = 254016 \) (not correct)
None of the evaluated options are consistent with the given points, meaning one or more data points might need reevaluation or there might be an issue with the options provided. The expected behavior of the curve should show a significant decline toward 0 as the x-values increase, considering that it does not cross the x-axis.
If further clarification or options are provided, the correct exponential equation can be determined more accurately. Based on the points given, it might also require constructing an exponential equation from the beginnings of its form \( y = ab^x \) using those specific points to find the values accordingly.