To find \( f(1) \) using the function rule \( f(x) = 7(2)^x + 10 \), we substitute \( x = 1 \) into the function.
\[ f(1) = 7(2)^1 + 10 \]
Calculating \( (2)^1 \):
\[ (2)^1 = 2 \]
Now, substitute this value back into the equation:
\[ f(1) = 7 \cdot 2 + 10 \]
Calculating \( 7 \cdot 2 \):
\[ 7 \cdot 2 = 14 \]
Adding 10:
\[ f(1) = 14 + 10 = 24 \]
Therefore,
\[ f(1) = 24 \]