Question

PLEASE HELP NEED THIS ANSWERED CORRECTLY

Answer 1

f(3) = 1.9

Solution:

Given function:

$f(x)=\frac{14}{7+2 e^{-0.6 x}}$

To find f(3):

Substitute x = 3 in the given function.

$f(3)=\frac{14}{7+2 e^{-0.6 (3)}}$

$f(3)=\frac{14}{7+2 e^{-1.8}}$

Let us first simplify $2e^{-1.8}$.

Apply exponent rule: $a^{-b}=\frac{1}{a^{b}}$

$2e^{-1.8}=2\frac{1}{e^{1.8}}$

The value of $e^{1.8}=6.04964$. (using calculator)

$\frac{2}{e^{1.8}}=\frac{2}{6.04964}=0.33059$

$2e^{-1.8}=0.33059$

Substitute this value in f(3).

$f(3)=\frac{14}{7+0.33059}$

$f(3)=\frac{14}{7.33059}$  

$f(3)=1.90980$

f(3) = 1.9

Hence the value of f(3) is 1.9.