Use the table to answer the question.

x f(x)

0 3
1 3.6
2 4.32
3 5.18
4 ?

5 7.46
Find the missing value in the table for the exponential function f(x)=3(1.2)x
. Round your answer to two decimal places.

(1 point)

1 answer

To find the missing value of \( f(x) \) for \( x = 4 \) using the given exponential function \( f(x) = 3(1.2)^x \), we can substitute \( x = 4 \) into the function.

Calculating \( f(4) \):

\[ f(4) = 3(1.2)^4 \]

Now, calculate \( (1.2)^4 \):

\[ (1.2)^4 = 1.2 \times 1.2 \times 1.2 \times 1.2 \]

Calculating step-by-step:

  1. \( 1.2 \times 1.2 = 1.44 \)
  2. \( 1.44 \times 1.2 = 1.728 \)
  3. \( 1.728 \times 1.2 = 2.0736 \)

Now plug this back into the equation:

\[ f(4) = 3 \times 2.0736 = 6.2208 \]

Rounding to two decimal places:

\[ f(4) \approx 6.22 \]

Thus, the missing value in the table for \( x = 4 \) is:

\[ \boxed{6.22} \]