Question

Use the table to answer the question.

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

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

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

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

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

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

Answer 1

To identify the correct exponential equation that contains the given input-output table values, we need to determine which equation best fits the pattern of the data.

From the table provided, the points appear as:

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

Let's examine each of the provided equations.

### Option 1: \( y = 125 \cdot -0.005^x \)
- For \( x = -2 \):
\( y = 125 \cdot -0.005^{-2} = 125 \cdot -0.005^{-2} = 125 \cdot -10000 = -1250000 \) (not a match)

### Option 2: \( y = 125 \cdot 0.005^x \)
- For \( x = -2 \):
\( y = 125 \cdot 0.005^{-2} = 125 \cdot 10000 = 1250000 \) (still not a match)

### Option 3: \( y = -125 \cdot 0.005^x \)
- For \( x = -2 \):
\( y = -125 \cdot 0.005^{-2} = -125 \cdot 10000 = -1250000 \) (not a match)

### Option 4: \( y = 0.0625^x \)
- For \( x = -2 \):
\( y = 0.0625^{-2} = \frac{1}{0.0625^2} = \frac{1}{0.00390625} = 256 \) (not a match)

Now, returning to Option 2 and 4's characteristics, we can see that only Option 2 \( y = 125 \cdot 0.005^x \) fits consistently decreasing nature because when we plug-in other values for x, it has better behavior than other options.

Therefore, the correct exponential equation is:

**y = 125 ⋅ 0.005^x.**