To find the missing value for \( f(4) \) using the given exponential function \( f(x) = 3(1.2)^x \), we can substitute \( x = 4 \) into the equation.
\[ f(4) = 3(1.2)^4 \]
Now, we need to calculate \( (1.2)^4 \):
\[ (1.2)^4 = 1.2 \times 1.2 \times 1.2 \times 1.2 \] Calculating step-by-step:
- \( 1.2 \times 1.2 = 1.44 \)
- \( 1.44 \times 1.2 = 1.728 \)
- \( 1.728 \times 1.2 = 2.0736 \)
Now we can use this result to find \( f(4) \):
\[ f(4) = 3 \times 2.0736 = 6.2208 \]
Finally, rounding to two decimal places, we have:
\[ f(4) \approx 6.22 \]
Thus, the missing value in the table is:
\[ \boxed{6.22} \]
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