Question

What is equation shown in the graph? (1, 10.5) (0, 10)
(1 point) Responses y=10⋅(1.05)x y is equal to 10 times 1 point 0 5 to the x th power 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 is equal to negative 10 times 1 point 0 5 to the x th power y=10⋅−(1.05)x

Answer 1

To determine the equation based on the points (1, 10.5) and (0, 10), we can analyze them further.

1. The point (0, 10) indicates that when \(x = 0\), \(y = 10\). This suggests that the function might be of the form \(y = a \cdot (b)^x\) where \(a = 10\).

2. The point (1, 10.5) provides a second condition. Substituting \(x = 1\) and \(y = 10.5\) into the general form gives us:

\[
10.5 = 10 \cdot (b)^1
\]

This simplifies to:

\[
b = \frac{10.5}{10} = 1.05
\]

Thus, we have determined that:

- The base \(b\) is \(1.05\)
- The initial value \(a\) is \(10\)

This results in the equation:

\[
y = 10 \cdot (1.05)^x
\]

Looking at your responses, the correct equation is:

**y = 10 ⋅ (1.05)^x**

This matches with the first option you provided.