Question

Which of the following exponential equations contains the points (-2,50) and (1,3.2)? y=8*4^x B.y=8*0.4 C y=-8 *0.4^x

Answer 1

To determine which of the given exponential equations contains the points \((-2, 50)\) and \((1, 3.2)\), we can plug in the \(x\)-values from each point into the equations and see if the resulting \(y\)-values match the corresponding \(y\)-values.

Let's evaluate each option one by one:

### Option A: \(y = 8 \cdot 4^x\)

1. For \((-2, 50)\):
\[
y = 8 \cdot 4^{-2} = 8 \cdot \frac{1}{16} = \frac{8}{16} = 0.5 \quad \text{(not 50)}
\]

2. For \((1, 3.2)\):
\[
y = 8 \cdot 4^{1} = 8 \cdot 4 = 32 \quad \text{(not 3.2)}
\]

### Option B: \(y = 8 \cdot 0.4\)

This option does not contain \(x\) in the equation. It simplifies to:
\[
y = 8 \cdot 0.4 = 3.2
\]
However, this will not produce a different \(y\)-value for different \(x\)-values, so it will not work for the points given.

### Option C: \(y = -8 \cdot 0.4^x\)

1. For \((-2, 50)\):
\[
y = -8 \cdot 0.4^{-2} = -8 \cdot \frac{1}{0.16} = -8 \cdot 6.25 = -50 \quad \text{(not 50)}
\]

2. For \((1, 3.2)\):
\[
y = -8 \cdot 0.4^{1} = -8 \cdot 0.4 = -3.2 \quad \text{(not 3.2)}
\]

### Summary:
- None of the equations accurately reproduce the coordinates given by the points \((-2, 50)\) and \((1, 3.2)\).

None of the given options correspond exclusively to the requirements posed by the points.