Question

Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.

x = 27/16
x = 13/8
x = 25/16
x = 7/4

Answer 1

it's 27/16

Explanation:

got it right on the test

Answer 2

x=25/16

Explanation:

Approximate Roots of Functions:

We are required to find the root of

`\displaystyle 5^(-x)+7=\ 2x+4`

Let's construct a function

`\displaystyle f(x)=\ 5^(-x)+7-2x-4`

Reducing:

`\displaystyle f(x)= 5^(-x)-2x+3`

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)

`\displaystyle f(1.5)=5^(-1.5)-2(1.5)+3\ =0.089`

We'll move up on x=1.52

`\displaystyle f(1.52)=5^(-1.52)-2(1.52)+3=\ 0.046`

We are closer to the solution, let's try some more up

`\displaystyle f(1.54)=5^(-1.54)-2(1.54)+3=\ 0.0038`

This value x=1.54 is close enough to the solution of the original equation

From the options given,
`(25)/(16)` is the closest to our solution

`\boxed{Answer:\ x=25/16}`