Chapter 11.5, Problem 49HP

To determine

Is either of them correct

Answer to Problem 49HP

The Marcus is correct because $x_0,x_1,and{x}_3$ are the first three iterates

Explanation of Solution

Given information:

Marcus and Armando are finding the first three iterates of $f\left(x\right)=5x-3\text{and}{x}_0=4$

  

Concept used:

A recursive formula is used to express any term of the sequence in terms of the previous term, provided that the first term is given.

Calculation:

In order to find the first three iterates $x_1,x_2\text{and}{x}_3$ as shown below

  $\begin{array}{c}f\left(x\right)=5x-3\\ x_0=4\\ f\left(x_1\right)=5x_0-3=5\left(4\right)-3\\ =20-3\\ =17\\ f\left(x_2\right)=5x_1-3=5\left(17\right)-3\\ =85-3\\ =82\end{array}$

The first three iterates are $4,17,and82$

Thus, the Marcus is correct because $x_0,x_1,and{x}_3$ are the first three iterates