Question

PLEASE HELP NEED THIS ANSWERED CORRECTLY

Answer 1

f(3) = 1.9

Solution:

Given function:

`$f(x)=(14)/(7+2 e^(-0.6 x))`

To find f(3):

Substitute x = 3 in the given function.

`$f(3)=(14)/(7+2 e^(-0.6 (3)))`

`$f(3)=(14)/(7+2 e^(-1.8))`

Let us first simplify
`2e^(-1.8)`.

Apply exponent rule:
`a^(-b)=(1)/(a^(b))`

`$ 2e^(-1.8)=2(1)/(e^(1.8))$`

The value of
`e^(1.8)=6.04964`. (using calculator)

`$(2)/(e^(1.8))=(2)/(6.04964)=0.33059`

`2e^(-1.8)=0.33059`

Substitute this value in f(3).

`$f(3)=(14)/(7+0.33059)`

`$f(3)=(14)/(7.33059)`

`$f(3)=1.90980`

f(3) = 1.9

Hence the value of f(3) is 1.9.