Professor Brown performed the same kind of experiment as...

Professor Brown performed the same kind of experiment as described in Problem $83,$ except that he replaced the food in the goal box with a mild electric shock. With the same kind of apparatus, he was able to measure the avoidance strength relative to the distance from the object to be avoided. He found that the avoidance strength $a$ (measured in grams) was related to the distance $d$ that the rat was from the shock (measured in centimeters) approximately by the equation $$ a=-\frac{4}{3} d+230 \quad 30 \leq d \leq 170 $$ If the same rat were trained as described in this problem and in Problem $83,$ at what distance (to one decimal place) from the goal box would the approach and avoidance strengths be the same? (What do you think the rat would do at this point?)

Professor Brown performed the same kind of experiment as described in Problem $83,$ except that he replaced the food in the goal box with a mild electric shock. With the same kind of apparatus, he was able to measure the avoidance strength relative to the distance from the object to be avoided. He found that the avoidance strength $a$ (measured in grams) was related to the distance $d$ that the rat was from the shock (measured in centimeters) approximately by the equation
$$
a=-\frac{4}{3} d+230 \quad 30 \leq d \leq 170
$$
If the same rat were trained as described in this problem and in Problem $83,$ at what distance (to one decimal place) from the goal box would the approach and avoidance strengths be the same? (What do you think the rat would do at this point?)

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Key Concepts

Linear Functions

Linear functions describe relationships between two variables that change at a constant rate. They are often represented by equations of the form y = mx + b, where m is the slope and b is the y-intercept. This concept is crucial in analyzing and predicting behaviors in experiments that involve proportional changes between factors, such as the relationship between stimulus intensity and response strength.

Intersection of Functions

The intersection of functions refers to the point or points at which two functions attain the same value for the dependent variable, given the same input of the independent variable. In experimental contexts, finding this intersection can help identify a balance point or equilibrium, where two competing influences, such as approach and avoidance tendencies, are equal.

Equilibrium Point in Behavioral Conflict

In studies of behavior, particularly those that involve conflicting motivations like approach and avoidance, an equilibrium point is reached when the drives for two opposing actions are balanced. At this point, the motivational forces counteract each other, leading to a state of indecision or hesitation, which can be critical for understanding how organisms resolve conflicts in decision making.

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