Question

Which exponential equation contains the points shown in the input-output table?

x y
−2
5,000,000
1 0.625
(1 point)
Responses

y=125⋅0.005x
y is equal to 125 times 0 point 0 0 5 to the x th power

y=0.0625x
y is equal to 0 point 0 6 2 5 to the x th power

y=−125⋅0.005x
y is equal to negative 125 times 0 point 0 0 5 to the x th power

y=125⋅−0.005x
y is equal to 125 times negative 0 point 0 0 5 to the x th power

Answer 1

To determine which exponential equation fits the points given in the table, we need to analyze the two points provided:

1. For \( x = -2 \), \( y = 5,000,000 \)
2. For \( x = 1 \), \( y = 0.625 \)

Let's use these points to check the given options.

### Option 1: \( y = 125 \cdot 0.005^x \)

- For \( x = -2 \):
\[
y = 125 \cdot 0.005^{-2} = 125 \cdot (1/0.005^2) = 125 \cdot 40000 = 5,000,000 \quad \text{(correct)}
\]
- For \( x = 1 \):
\[
y = 125 \cdot 0.005^1 = 125 \cdot 0.005 = 0.625 \quad \text{(correct)}
\]

### Option 2: \( y = 0.0625^x \)

- For \( x = -2 \):
\[
y = 0.0625^{-2} = 1/0.0625^2 = 1/0.00390625 \approx 256 \quad \text{(not correct)}
\]

### Option 3: \( y = -125 \cdot 0.005^x \)

- For \( x = -2 \):
\[
y = -125 \cdot 0.005^{-2} = -125 \cdot 40000 = -5,000,000 \quad \text{(not correct)}
\]

### Option 4: \( y = 125 \cdot -0.005^x \)

- For \( x = -2 \):
\[
y = 125 \cdot (-0.005)^{-2} = 125 \cdot 40000 = 5,000,000 \quad \text{(not correct due to the negative)}
\]
- For \( x = 1 \):
\[
y = 125 \cdot (-0.005)^1 = 125 \cdot -0.005 = -0.625 \quad \text{(not correct)}
\]

From the analysis above, only the first option \( y = 125 \cdot 0.005^x \) fits both points.

Thus, the correct equation is:

\[
\boxed{y = 125 \cdot 0.005^x}
\]