Exponential Functions from Situations Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items

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)=
Remaining Attempts : 3
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Answer 1

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

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

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

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

Calculating this 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,

\[ (1.2)^4 \approx 2.0736 \]

Now, we multiply by 3:

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

Rounding this to two decimal places:

\[ f(4) \approx 6.22 \]

So the missing value in the table for \( f(4) \) is approximately 6.22.