g(x) = e^{x − 1} + 2x − 15

a. Show that the equation g(x) = 0 can be written as

The root of g(x) = 0 is α. The iterative formula x_{n + 1} = ln (15 − 2x_n) + 1, x₀ = 3, is used to find a value for α.

b. Calculate the values of x₁, x₂ and x₃ to 4 decimal places.

c. By choosing a suitable interval, show that α = 3.16 correct to 2 decimal places.

15 x = ln (15 - 2x) + 1, x < - 2