The solution to the equation above using three iterations of successive approximation is x = 25/16
The solution of an equation is the true values of the equation
The equation is given as:
[tex]5^{-x} + 7 =2x + 4[/tex]
Equate to 0
[tex]5^{-x} + 7 -2x - 4 = 0[/tex]
Write the equation as a function
[tex]f(x) = 5^{-x} + 7 -2x - 4[/tex]
The equation has a solution only when the function f(x) equals 0.
From the graph, we have:
x = 1.5
So, we have:
[tex]f(1.5) = 5^{-1.5} + 7 -2*1.5 - 4[/tex]
Evaluate
f(1.5) = 0.089
Set x to 1.52 to determine a closer value of f(x) to 0.
[tex]f(1.52) = 5^{-1.52} + 7 -2*1.52 - 4[/tex]
Evaluate
f(1.52) = 0.047
Set x to 1.54 to determine a closer value of f(x) to 0.
[tex]f(1.54) = 5^{-1.54} + 7 -2*1.54 - 4[/tex]
Evaluate
f(1.54) = 0.004
Notice that 0.004 is closer to 0 than 0.047 and 0.089
The closest value to 1.54 is 25/16 in the given options
Hence, the solution to the equation above using three iterations of successive approximation is x = 25/16
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