Suppose $ N $ is the number of people in the United States who travel by car to another state for a vacation this year when the average price of gasoline is $ p $ dollars per gallon. Do you expect $ dN/dp $ to be positive or negative? Explain.
A negative divided by a positive will equal a negative.
In this problem, we have n the variable end is the number of people traveling by car on vacation. T is the price in dollars per gallon of gas? And we wanted to determine if this derivative would be positive or negative. Uh So how does, um uh and a number of people traveling by car change with respect to a change in the price of gas? Well as gas increases, the number of people traveling by car is going to decrease, because if it's more expensive to travel, because it costs more for gas, uh not as many people are going to decide to travel. So if the price of gas is increasing, the number of people traveling is decreasing. So you can think of this as a negative amount over a positive amount. And so this derivative Is going to be negative or less than zero.