To find the y-intercept of the function \( f(x) = 9.5(2.6)^x \), we need to evaluate the function at \( x = 0 \). The y-intercept occurs where the graph of the function crosses the y-axis, which is when \( x = 0 \).
Let's calculate \( f(0) \):
\[ f(0) = 9.5(2.6)^0 \]
We know that any number raised to the power of 0 is 1:
\[ (2.6)^0 = 1 \]
So, substituting that into the equation, we get:
\[ f(0) = 9.5 \times 1 = 9.5 \]
Therefore, the value of the y-intercept of the graph of \( f(x) = 9.5(2.6)^x \) is
\[ \boxed{9.5}. \]
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