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)=
Remaining Attempts : 3
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page 15 of 16

Answer 1

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

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

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

Now substituting that back into the function:

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

Rounding to two decimal places:

\[ f(4) \approx 6.22 \]

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

\[ \boxed{6.22} \]