Question
For the function \( f(x)=6 e^{x} \), calculate the following function values: \( f(-4)=\square \) \( f(-1)=\square \) \( f(0)=\square \) \( f(1)=\square \) \( f(4)=\square \) Submit Question
Ask by Clarke Cervantes. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(-4) = \frac{6}{e^4} \), \( f(-1) = \frac{6}{e} \), \( f(0) = 6 \), \( f(1) = 6e \), \( f(4) = 6e^4 \).
Solution
1. Evaluate \( f(-4) \):
\[
f(-4) = 6e^{-4} = \frac{6}{e^4}
\]
2. Evaluate \( f(-1) \):
\[
f(-1) = 6e^{-1} = \frac{6}{e}
\]
3. Evaluate \( f(0) \):
\[
f(0) = 6e^{0} = 6
\]
4. Evaluate \( f(1) \):
\[
f(1) = 6e^{1} = 6e
\]
5. Evaluate \( f(4) \):
\[
f(4) = 6e^{4}
\]
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Simplify this solution Mind Expander
To find the function values for \( f(x) = 6 e^{x} \), we’ll plug in the respective values of \( x \) into the function. 1. \( f(-4) = 6 e^{-4} \approx 6 \times 0.01832 \approx 0.1099 \) 2. \( f(-1) = 6 e^{-1} \approx 6 \times 0.3679 \approx 2.2074 \) 3. \( f(0) = 6 e^{0} = 6 \times 1 = 6 \) 4. \( f(1) = 6 e^{1} \approx 6 \times 2.7183 \approx 16.3098 \) 5. \( f(4) = 6 e^{4} \approx 6 \times 54.5982 \approx 327.5892 \) So, the function values are: - \( f(-4) \approx 0.1099 \) - \( f(-1) \approx 2.2074 \) - \( f(0) = 6 \) - \( f(1) \approx 16.3098 \) - \( f(4) \approx 327.5892 \)
