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)=
Answers
GPT-4o mini
To find the missing value \( f(4) \) in the table using the exponential function \( f(x) = 3(1.2)^x \), we need to substitute \( x = 4 \) into the function.
Let's calculate it step by step:
1. Calculate \( (1.2)^4 \):
\[
(1.2)^4 = 1.2 \times 1.2 \times 1.2 \times 1.2 = 2.0736
\]
2. Now, substitute this value into the function:
\[
f(4) = 3(1.2)^4 = 3 \times 2.0736
\]
3. Calculate \( 3 \times 2.0736 \):
\[
f(4) = 6.2208
\]
4. Finally, round to two decimal places:
\[
f(4) \approx 6.22
\]
Thus, the missing value in the table is \( f(4) = 6.22 \).
Let's calculate it step by step:
1. Calculate \( (1.2)^4 \):
\[
(1.2)^4 = 1.2 \times 1.2 \times 1.2 \times 1.2 = 2.0736
\]
2. Now, substitute this value into the function:
\[
f(4) = 3(1.2)^4 = 3 \times 2.0736
\]
3. Calculate \( 3 \times 2.0736 \):
\[
f(4) = 6.2208
\]
4. Finally, round to two decimal places:
\[
f(4) \approx 6.22
\]
Thus, the missing value in the table is \( f(4) = 6.22 \).