Question

Use the graph to answer the question.

The graph shows an exponentially decreasing line passing through (0, 8) and (1, 6)

Write the exponential equation shown in the graph.

Answer 1

To write the exponential equation of the form \( y = ab^x \), we can use the information from the two points given: (0, 8) and (1, 6).

1. We know that at \( x = 0 \), \( y = 8 \). This means:
\[
y = ab^0 \implies 8 = a \cdot 1 \implies a = 8
\]

2. Now we can use the point (1, 6) to find \( b \). We substitute \( a = 8 \) and \( x = 1 \) into the equation:
\[
y = 8b^1 \implies 6 = 8b
\]
To solve for \( b \), we divide both sides by 8:
\[
b = \frac{6}{8} = \frac{3}{4}
\]

3. Now that we have both \( a \) and \( b \), we can write the exponential equation:
\[
y = 8 \left( \frac{3}{4} \right)^x
\]

Thus, the exponential equation shown in the graph is:
\[
y = 8 \left( \frac{3}{4} \right)^x
\]