Question

Consider the following equation.5^(-x) + 7 = 2x +4Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point

Answer 1

5^(-x) + 7 = 2x +4

Approximate the roots of the function:

First, construct a function:

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

Combine like terms

f(x)= 5^(-x) -2x +3

Use the crossing point given by the graph x=1.5

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

Move up to x= 1.52

f(1.52)= 0.046

Move up to x= 1.54

f(1.54)= 0.038

x=1.54 is close enough to the solution

From the options given , the closer solution is 25/16