f(3) = 1.9
Solution:
Given function:
[tex]$f(x)=\frac{14}{7+2 e^{-0.6 x}}[/tex]
To find f(3):
Substitute x = 3 in the given function.
[tex]$f(3)=\frac{14}{7+2 e^{-0.6 (3)}}[/tex]
[tex]$f(3)=\frac{14}{7+2 e^{-1.8}}[/tex]
Let us first simplify [tex]2e^{-1.8}[/tex].
Apply exponent rule: [tex]a^{-b}=\frac{1}{a^{b}}[/tex]
[tex]$ 2e^{-1.8}=2\frac{1}{e^{1.8}}$[/tex]
The value of [tex]e^{1.8}=6.04964[/tex]. (using calculator)
[tex]$\frac{2}{e^{1.8}}=\frac{2}{6.04964}=0.33059[/tex]
[tex]2e^{-1.8}=0.33059[/tex]
Substitute this value in f(3).
[tex]$f(3)=\frac{14}{7+0.33059}[/tex]
[tex]$f(3)=\frac{14}{7.33059}[/tex]
[tex]$f(3)=1.90980[/tex]
f(3) = 1.9
Hence the value of f(3) is 1.9.
