Question

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)
f(4)=

Answer 1

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

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

Now, we 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, substituting back into the function:

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

Rounding to two decimal places:

\[
f(4) \approx 6.22
\]

Therefore, the missing value \( f(4) \) is:

\[
\boxed{6.22}
\]