What is the equation shown in the graph?

Question

(0, 10) (1, 10.5)

(1 point)
Responses

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

y=−10⋅(1.05)x
𝑦
=
−
10
⋅
(
1.05
)
𝑥
y is equal to negative 10 times 1 point 0 5 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=10⋅−(1.05)x

Answer 1

To determine the correct equation based on the given points (0, 10) and (1, 10.5), we can analyze the points in relation to the equations provided.

1. The point (0, 10) indicates that when \(x = 0\), \(y\) should equal 10.
2. The point (1, 10.5) indicates that when \(x = 1\), \(y\) should equal 10.5.

Let's check each option:

1. \(y = 1.05 \cdot (10)^x\):

   • For \(x = 0\): \(y = 1.05 \cdot (10)^0 = 1.05 \cdot 1 = 1.05\) (not a match).

2. \(y = -10 \cdot (1.05)^x\):

   • For \(x = 0\): \(y = -10 \cdot (1.05)^0 = -10 \cdot 1 = -10\) (not a match).

3. \(y = 10 \cdot (1.05)^x\):

   • For \(x = 0\): \(y = 10 \cdot (1.05)^0 = 10 \cdot 1 = 10\) (match).
   • For \(x = 1\): \(y = 10 \cdot (1.05)^1 = 10 \cdot 1.05 = 10.5\) (also a match).

4. \(y = 10 \cdot - (1.05)^x\):

   • For \(x = 0\): \(y = 10 \cdot - (1.05)^0 = 10 \cdot -1 = -10\) (not a match).

Based on this analysis, the correct equation that matches the points given is:

\(y = 10 \cdot (1.05)^x\).