Homework SourseIn the bisection method if the interval is 4 6 and you want
In the bisection method, if the interval is [4, 6] and you want to have an error of 0.0001, how many iterations would you need? Use the formula 1/2^n(b - a) lessthanorequalto element and solve for n. 15 14 13 16![In the bisection method, if the interval is [4, 6] and you want to have an error of 0.0001, how many iterations would you need? Use the formula 1/2^n(b - a) le](/WebImages/44/in-the-bisection-method-if-the-interval-is-4-6-and-you-want-1139066-1761610466-0.webp "In the bisection method, if the interval is [4, 6] and you want to have an error of 0.0001, how many iterations would you need? Use the formula 1/2^n(b - a) le")
Solution
Answer: 14
Proof:
Given error is 0.0001 = 10^-4
By using 1/2^n * (b-a) = 2^-n * (b-a)
= 2 * 2^-n = 2^(1-n)
2^(1-n) < 10^-4 = (-n+1) (log2)base 10 < -4
= n-1 (log2)base 10 > 4
= n-1 > (4/(log2)base10)
(log2)base10 = 0.301029
= n-1 > 4/0.301029 = n > 13 +1 = 14
