Question

Let f (2) = the number of people riding subway daily from Silver Spring, Maryland to U-street, DC when the fare is x cents. If f (250) = 5000, f' (250) = -50, then write down the approximate number of passengers, when the fare is increased to $2.60.

a. 4650
b. 3980
c. 2870
d. 4509

Answer 1

The approximate number of passengers when the fare is increased to $2.60 is calculated using linear approximation and the given rate of change in ridership, resulting in 4500 passengers.

Step-by-step explanation:

The student is asking a question related to the application of derivatives in the context of a real-world problem. Given that f(250) = 5000 represents the number of people riding the subway at a fare of 250 cents (or $2.50) and f'(250) = -50 is the rate of change in ridership per cent increase in fare, we can approximate the number of passengers when the fare is increased to $2.60 using linear approximation.

First, let's find the change in fare from $2.50 to $2.60, which is 260 cents - 250 cents = 10 cents. Applying the rate of change, we get the approximate change in passengers as 10 cents × (-50 passengers/cent) = -500 passengers.

Subtracting this change from the original number of passengers, we get 5000 passengers - 500 passengers = 4500 passengers. Thus, the approximate number of passengers when the fare is increased to $2.60 is 4500.