Chapter 4.5, Problem 16P

Reasoning Write a rule that is an example of a nonlinear function that fits the following description.

When b is 49, a is 7, and a is a function of b.

To determine

To write: A rule that is an example of a nonlinear function that fits a given condition

Answer to Problem 16P

  $a=b^2-2394$

Explanation of Solution

Given:

When b is 49, a is 7, and a is a function of b.

We must have a as a function of b, i.e. $a=f(b)$ and f(b) must be a nonlinear function.

Let us consider $a=b^2-2394$ . Then, $f(b)=b^2-2394$ is a nonlinear function and

  $\begin{array}{l}f(49)={49}^2-2394\\ =>f(49)=2401-2394=7\end{array}$

Thus, $a=7$ when $b=49$ .