Chapter 5.1, Problem 60E

New ton’s method seeks to approximate a solution f(x) = 0 that starts with an initial approximation x₀and successively defines a sequence $z_{n+1}=x_n-\frac{f\left(x_n\right)}{f\text{'}\left(x_n\right)}$ . For the given choice of f and x₀. write out the formula for $x_{n+1}$ . If the sequence appeals to converge, give an exact formula for the solution x. then identify the limit x accurate to four decimal places and the smallest ii such that x_nagrees with x up to four decimal places.

60. [T] A bank account earns 5% interest compounded monthly. Suppose that S 1000 is initially deposited into the account, but that $ 1 0 is withdrawn each month.

a. Show that the amount in the account after n months is $A_n=\left(1-.05/12\right)A_{n-1}-10;$

   $A_0=1000$

b. How much money will be in the account after I year?

c. Is the amount increasing or decreasing?

d. Suppose that instead of $10. a fixed amount d

dollars is withdrawn each month. Find a value of d such that the amount in the account after each month remains $1000.

e. What happens if d is greater than this amount?