x f(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
𝑓
(
𝑥
)
=
3
(
1.2
)
𝑥
. Round your answer to two decimal places.

(1 point)
f(4)=

1 answer

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

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

First, we need to calculate \( (1.2)^4 \):

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

Calculating it step by step:

\[ 1.2 \times 1.2 = 1.44 \]

Next, multiply \( 1.44 \) by \( 1.2 \):

\[ 1.44 \times 1.2 = 1.728 \]

Then, multiply \( 1.728 \) by \( 1.2 \):

\[ 1.728 \times 1.2 = 2.0736 \]

Now we multiply this by 3:

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

Rounding to two decimal places, we have:

\[ f(4) \approx 6.22 \]

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

\[ \boxed{6.22} \]