To find the y-intercept of the function \( f(x) = 10.5(3.6)^{x} \), we need to evaluate the function when \( x = 0 \):
\[ f(0) = 10.5(3.6)^{0} \]
Since any non-zero number raised to the power of 0 is 1:
\[ f(0) = 10.5 \cdot 1 = 10.5 \]
Therefore, the value of the y-intercept is \( 10.5 \).
The correct answer is:
c. 10.5