Use the table to answer the question.

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)
f(4)=__

Answer 1

To find the missing value for \( f(4) \) in the exponential function \( f(x) = 3(1.2)^x \), we will substitute \( x = 4 \) into the function.

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

First, let's 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. \( 1.728 \times 1.2 = 2.0736 \)

So, \( (1.2)^4 = 2.0736 \).

Now, substituting this back into the function:

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

Finally, rounding \( 6.2208 \) to two decimal places:

\[ f(4) \approx 6.22 \]

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

f(4) = 6.22