Question

Suppose N is the number of people in the United States who travel by car to another state for a vacation in a year when the average price of gasoline is p dollars per gallon. Do you expect \(\frac{{{\bf{d}}N}}{{{\bf{d}}p}}\) to be positive or negative? Explain.

Short answer

\(\frac{{{\rm{d}}N}}{{{\rm{d}}p}}\) represents the rate at which the number of people traveling by car to another state for vacation changes regarding gasoline prices. As the prices of gasoline are increasing, the number of people who are traveling is decreasing—the \(\frac{{{\rm{d}}N}}{{{\rm{d}}p}}\) expected as negative.

Step-by-step solution

Meaning of \(\frac{{{\bf{d}}N}}{{{\bf{d}}p}}\)

The expression \(\frac{{{\rm{d}}N}}{{{\rm{d}}p}}\) represents the rate at which the number of people traveling by car to another state for vacation changes regarding gasoline prices.

Intepretation of \(\frac{{{\bf{d}}N}}{{{\bf{d}}p}}\)

With the increase in gasoline price, we expect fewer people to travel so that the expression \(\frac{{{\rm{d}}N}}{{{\rm{d}}p}}\) can attain a negative value.

Thus, we expect \(\frac{{{\rm{d}}N}}{{{\rm{d}}p}}\) as negative.