Question

Use the graph to answer the question.

The graph shows an exponentially rising line passing through (0, 10) and (1, 10.5)

Write the exponential equation shown in the graph.

Answer 1

To write the exponential equation of the form \( y = a \cdot b^x \), we need to determine the values of \( a \) and \( b \).

From the graph, we know that:
- The point \( (0, 10) \) indicates that when \( x = 0 \), \( y = 10 \). This tells us that \( a = 10 \) because \( y = a \cdot b^0 = a \).

So, we have:
\[
y = 10 \cdot b^x
\]

Next, we use the point \( (1, 10.5) \) to find \( b \):
\[
10.5 = 10 \cdot b^1
\]
Dividing both sides by 10 gives:
\[
b = \frac{10.5}{10} = 1.05
\]

Now, we can substitute \( a \) and \( b \) into the equation:
\[
y = 10 \cdot 1.05^x
\]

Therefore, the exponential equation shown in the graph is:
\[
y = 10 \cdot 1.05^x
\]