Question

Use the graph to answer the question.

(-1, 10) (1, 3.6)

Which equation is shown in the graph?

(1 point)
Responses

y=6⋅(0.6)x
𝑦
=
6
⋅
(
0.6
)
𝑥
y is equal to 6 times 0 point 6 to the x th power

y=10⋅(1.05)x
𝑦
=
10
⋅
(
1.05
)
𝑥
y is equal to 10 times 1 point 0 5 to the x th power

y=6⋅0.6x
𝑦
=
6
⋅
0.6
𝑥
y is equal to 6 times 0 point 6 x

y=6⋅(3.6)x

Answer 1

To determine which equation represents the graph that includes the points (-1, 10) and (1, 3.6), we can analyze the equations and see which one passes through those points.

1. **Calculate the value of y for each equation at x = -1 and x = 1**.

For the first equation:
**y = 6⋅(0.6)^x**
- At x = -1:
\( y = 6 \cdot (0.6)^{-1} = 6 \cdot \frac{1}{0.6} = 6 \cdot \frac{10}{6} = 10 \) (correct)
- At x = 1:
\( y = 6 \cdot (0.6)^1 = 6 \cdot 0.6 = 3.6 \) (correct)

For the second equation:
**y = 10⋅(1.05)^x**
- At x = -1:
\( y = 10 \cdot (1.05)^{-1} = 10 \cdot \frac{1}{1.05} \approx 9.52 \) (not correct)
- At x = 1:
\( y = 10 \cdot (1.05)^1 = 10 \cdot 1.05 = 10.5 \) (not correct)

For the third equation:
**y = 6⋅0.6^x**
- At x = -1:
\( y = 6 \cdot 0.6^{-1} = 6 \cdot \frac{1}{0.6} = 10 \) (correct)
- At x = 1:
\( y = 6 \cdot 0.6^1 = 6 \cdot 0.6 = 3.6 \) (correct)

For the fourth equation:
**y = 6⋅(3.6)^x**
- At x = -1:
\( y = 6 \cdot (3.6)^{-1} = 6 \cdot \frac{1}{3.6} \approx 1.67 \) (not correct)
- At x = 1:
\( y = 6 \cdot (3.6)^1 = 6 \cdot 3.6 = 21.6 \) (not correct)

From the calculations, both the first equation \( y = 6 \cdot (0.6)^x \) and the third equation \( y = 6 \cdot 0.6^x \) give the correct values for points (-1, 10) and (1, 3.6).

However, equations (1) and (3) are essentially the same, so either would be correct. The response choices can be confusing, but the correct answer here would be:

**y = 6⋅(0.6)^x** or **y = 6⋅0.6^x** (interpreted as they are the same).