Question

jeremiah lives in new york city and takes a taxi almost everywhere he goes. in order to calculate the price of his taxi ride, jeremiah came up with the equation ( p = 1.80lceil x
ceil+2.50 ), where ( x ) is the number of miles or partial miles traveled in the taxi. explain the meaning of the constant 2.50 as it relates to the situation. $2.50 is the base amount that jeremiah must pay in order for the taxi to pick him up before he has been driven anywhere. $2.50 is the amount jeremiah must pay as long as the taxi has not driven a complete mile. for every mile or partial mile the taxi drives, jeremiah must pay an additional $2.50. jeremiah must pay $2.50 plus $1.80, or $4.30, per mile for each taxi ride.

Explanation:

In the equation \(P = 1.80\lceil x
ceil+ 2.50\), the term \(1.80\lceil x
ceil\) represents the cost that depends on the number of miles (\(x\)) traveled (with the ceiling function \(\lceil x
ceil\) indicating that for any partial - mile, the cost is calculated as a full - mile cost). The constant term \(2.50\) is a fixed cost. In the context of a taxi ride, fixed costs are typically associated with the base fare (the amount charged just for getting into the taxi before any distance is traveled).

• Option 2: If \(x = 0\) (no miles traveled, but the taxi has picked him up), \(P=2.50\). If \(x\) is a partial mile (say \(x = 0.5\)), \(\lceil x

ceil=1\) and \(P=1.80\times1 + 2.50=4.30\). So it's not just for when the taxi has not driven a complete mile.

• Option 3: The coefficient of \(\lceil x

ceil\) (\(1.80\)) is the amount per mile or partial mile, not \(2.50\).

• Option 4: The cost per mile or partial mile is \(1.80\), and \(2.50\) is a separate fixed amount.

Answer:

\(\$2.50\) is the base amount that Jeremiah must pay in order for the taxi to pick him up before he has been driven anywhere.