Answer:
x=25/16
Step-by-step explanation:
Approximate Roots of Functions:
We are required to find the root of
[tex]\displaystyle 5^{-x}+7=\ 2x+4[/tex]
Let's construct a function
[tex]\displaystyle f(x)=\ 5^{-x}+7-2x-4[/tex]
Reducing:
[tex]\displaystyle f(x)= 5^{-x}-2x+3[/tex]
The equation will have a solution when f(x)=0. We'll start from the approximate crossing point given in the graph (x=1.5)
[tex]\displaystyle f(1.5)=5^{-1.5}-2(1.5)+3\ =0.089[/tex]
We'll move up on x=1.52
[tex]\displaystyle f(1.52)=5^{-1.52}-2(1.52)+3=\ 0.046[/tex]
We are closer to the solution, let's try some more up
[tex]\displaystyle f(1.54)=5^{-1.54}-2(1.54)+3=\ 0.0038[/tex]
This value x=1.54 is close enough to the solution of the original equation
From the options given, [tex]\frac{25}{16}[/tex] is the closest to our solution
[tex]\boxed{Answer:\ x=25/16}[/tex]
