To determine which exponential equation contains the points (0, 16) and (1, 6.4), let's analyze the potential options one by one:
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y = 6.4x: This is a linear equation, not exponential.
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y = 6.4^x: This would produce the points for x = 0 and x = 1 as:
- For x = 0: \(y = 6.4^0 = 1\) (does not match (0, 16))
- For x = 1: \(y = 6.4^1 = 6.4\) (matches (1, 6.4))
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y = 16 * 6.4^x: This equation includes a coefficient and will produce:
- For x = 0: \(y = 16 * 6.4^0 = 16 * 1 = 16\) (matches (0, 16))
- For x = 1: \(y = 16 * 6.4^1 = 16 * 6.4 = 102.4\) (does not match the second point)
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y = -16 * 0.4^x: This equation will yield:
- For x = 0: \(y = -16 * 0.4^0 = -16\) (does not match (0, 16))
- For x = 1: \(y = -16 * 0.4^1 = -6.4\) (does not match (1, 6.4))
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y = 16 * 0.4^x: For this equation:
- For x = 0: \(y = 16 * 0.4^0 = 16 * 1 = 16\) (matches (0, 16))
- For x = 1: \(y = 16 * 0.4^1 = 16 * 0.4 = 6.4\) (matches (1, 6.4))
Thus, the correct exponential equation that contains the points (0, 16) and (1, 6.4) is:
y = 16 * 0.4^x