Chapter 4.1, Problem 85E

Psychology. People approach certain situations with "mixed emotions." For example, public speaking often brings forth the positive response of recognition and the negative response of failure. Which dominates? J. S. Brown, in an experiment on approach and avoidance, trained rats by feeding them from a goal box. The rats received mild electric shocks from the same goal box. This established an approach-avoidance conflict relative to the goal box. Using an appropriate apparatus. Brown arrived at the following relationships:

$\begin{array}{l}p=-\frac{1}{5}d+70\text{ Approach equation}\\ p=-\frac{4}{3}d+230\text{Avoidance equation}\end{array}$

where $30\le d\le 172.5$. The approach equation gives the pull (in grams) toward the food goal box when the rat is placed $d$ centimeters away from it. The avoidance equation gives the pull (in grams) away from the shock goal box when

the rat is placed $d$ centimeters from it.

(A) Graph the approach equation and the avoidance equation in the same coordinate system.

(B) Find the value of $d$ for the point of intersection of these two equations.

(C) What do you think the rat would do when placed the distance $d$ from the box found in part (B)?