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 [tex]$P=1.80\lceil x\rceil+2.50$[/tex], where [tex]$x$[/tex] 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.

A. [tex][tex]$\$[/tex]2.50$[/tex] is the base amount that Jeremiah must pay in order for the taxi to pick him up before he has been driven anywhere.
B. [tex]$\[tex]$2.50$[/tex][/tex] is the amount Jeremiah must pay as long as the taxi has not driven a complete mile.
C. For every mile or partial mile the taxi drives, Jeremiah must pay an additional [tex]$\$2.50$[/tex].
D. Jeremiah must pay [tex]$\[tex]$2.50$[/tex][/tex] plus [tex]$\$1.80$[/tex], or [tex]$\[tex]$4.30$[/tex][/tex], per mile for each taxi ride.

Question

malaysiapollarliving malaysiapollarliving

18-07-2024
Mathematics

Answered

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 [tex]$P=1.80\lceil x\rceil+2.50$[/tex], where [tex]$x$[/tex] 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.

A. [tex][tex]$\$[/tex]2.50$[/tex] is the base amount that Jeremiah must pay in order for the taxi to pick him up before he has been driven anywhere.
B. [tex]$\[tex]$2.50$[/tex][/tex] is the amount Jeremiah must pay as long as the taxi has not driven a complete mile.
C. For every mile or partial mile the taxi drives, Jeremiah must pay an additional [tex]$\$2.50$[/tex].
D. Jeremiah must pay [tex]$\[tex]$2.50$[/tex][/tex] plus [tex]$\$1.80$[/tex], or [tex]$\[tex]$4.30$[/tex][/tex], per mile for each taxi ride.

Answer :

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Let's delve into the meaning of the constant 2.50 in the equation [tex]$ P = 1.80 \lceil x \rceil + 2.50 $[/tex].
In this context, [tex]$P$[/tex] represents the total price of the taxi ride, and [tex]$ x $[/tex] represents the number of miles or partial miles traveled.

The constant [tex]$2.50 represents the initial base fare that Jeremiah needs to pay just for the taxi to pick him up. This charge is incurred irrespective of the distance traveled. It is a fixed starting fee before any consideration of the distance. Therefore, the correct explanation is: "$[/tex]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."

This means Jeremiah will have to pay [tex]$2.50 as soon as he gets into the taxi, even if he travels zero miles. Additional charges will be calculated based on the distance traveled, with $ \lceil x \rceil $ representing the ceiling function that rounds $ x $ up to the nearest whole mile, and multiplying it by $[/tex]1.80.