Answer :
To find the value of [tex]\( f(x) \)[/tex] for [tex]\( f(x) = \frac{8}{1 + 3 e^{-0.7 x}} \)[/tex] when [tex]\( x = -1 \)[/tex], we need to follow these steps:
1. Substitute [tex]\( x = -1 \)[/tex] into the function:
[tex]\[ f(-1) = \frac{8}{1 + 3 e^{-0.7 \cdot (-1)}} \][/tex]
2. Simplify the exponent:
[tex]\[ -0.7 \cdot (-1) = 0.7 \][/tex]
3. Rewrite the function with the simplified exponent:
[tex]\[ f(-1) = \frac{8}{1 + 3 e^{0.7}} \][/tex]
4. Calculate [tex]\( e^{0.7} \)[/tex], this is approximately:
[tex]\[ e^{0.7} \approx 2.01375 \][/tex]
5. Substitute this value back into the denominator:
[tex]\[ f(-1) = \frac{8}{1 + 3 \cdot 2.01375} \][/tex]
6. Calculate the value inside the denominator:
[tex]\[ 3 \cdot 2.01375 = 6.04125 \][/tex]
[tex]\[ 1 + 6.04125 = 7.04125 \][/tex]
7. Divide the numerator by this result:
[tex]\[ f(-1) = \frac{8}{7.04125} \approx 1.1361605924567681 \][/tex]
8. Round this result to the nearest hundredth:
[tex]\[ 1.1361605924567681 \approx 1.14 \][/tex]
Thus, the value of [tex]\( f(-1) \)[/tex] rounded to the nearest hundredth is [tex]\( 1.14 \)[/tex].
1. Substitute [tex]\( x = -1 \)[/tex] into the function:
[tex]\[ f(-1) = \frac{8}{1 + 3 e^{-0.7 \cdot (-1)}} \][/tex]
2. Simplify the exponent:
[tex]\[ -0.7 \cdot (-1) = 0.7 \][/tex]
3. Rewrite the function with the simplified exponent:
[tex]\[ f(-1) = \frac{8}{1 + 3 e^{0.7}} \][/tex]
4. Calculate [tex]\( e^{0.7} \)[/tex], this is approximately:
[tex]\[ e^{0.7} \approx 2.01375 \][/tex]
5. Substitute this value back into the denominator:
[tex]\[ f(-1) = \frac{8}{1 + 3 \cdot 2.01375} \][/tex]
6. Calculate the value inside the denominator:
[tex]\[ 3 \cdot 2.01375 = 6.04125 \][/tex]
[tex]\[ 1 + 6.04125 = 7.04125 \][/tex]
7. Divide the numerator by this result:
[tex]\[ f(-1) = \frac{8}{7.04125} \approx 1.1361605924567681 \][/tex]
8. Round this result to the nearest hundredth:
[tex]\[ 1.1361605924567681 \approx 1.14 \][/tex]
Thus, the value of [tex]\( f(-1) \)[/tex] rounded to the nearest hundredth is [tex]\( 1.14 \)[/tex].
