Which exponential equation contains the points (0,16) and (1,6.4) ?(1 point) Responses y=6.4x y is equal to 6 point 4 to the x th power y=16⋅6.4x y is equal to 16 times 6 point 4 to the x th power y=−16⋅0.4x y is equal to negative 16 times 0 point 4 to the x th power y=16⋅0.4x

Answer 1

To determine which exponential equation contains the points (0, 16) and (1, 6.4), let's analyze the potential options one by one:

1. y = 6.4x: This is a linear equation, not exponential.

2. 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))

3. 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)

4. 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))

5. 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