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. $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.
B. $2.50 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]2.50[/tex] plus [tex]1.80[/tex], or [tex]4.30[/tex], per mile for each taxi ride.
Answer (2)
The equation for the taxi ride price is P = 1.80 ⌈ x ⌉ + 2.50 .
When the distance traveled is 0 miles ( x = 0 ), the price is P = 1.80 × 0 + 2.50 = 2.50 .
This means that $2.50 is the base fare that Jeremiah pays even before traveling any distance.
Therefore, the constant $2.50 represents the base amount Jeremiah must pay for the taxi to pick him up: $2.50 .
Explanation
Understanding the Equation We are given the equation P = 1.80 l ce i l x ⌉ + 2.50 , which calculates the price P of a taxi ride, where x is the number of miles or partial miles traveled. We need to explain the meaning of the constant 2.50 in this equation.
Calculating the Price for 0 Miles Let's consider the case when Jeremiah travels 0 miles. In this case, x = 0 . Substituting x = 0 into the equation, we get: P = 1.80 × ⌈ 0 ⌉ + 2.50 Since the ceiling function of 0 is 0, i.e., ⌈ 0 ⌉ = 0 , the equation becomes: P = 1.80 × 0 + 2.50 = 0 + 2.50 = 2.50 This means that even if Jeremiah travels 0 miles, the price of the taxi ride is $2.50 .
Interpreting the Constant This indicates that $2.50 is a base amount that Jeremiah must pay, regardless of the distance traveled. It can be interpreted as an initial charge or a fee for the taxi to pick him up. Therefore, the correct explanation is: $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.
Examples
Imagine you're taking a taxi. The $2.50 is like a starting fee, just for the taxi to come and get you. Then, for every bit of a mile you travel, you pay another $1.80. This kind of pricing is common in services where there's a fixed cost to start, plus a variable cost depending on how much you use. Understanding this helps you estimate the cost of your ride before you even start!
The constant $2.50 in the taxi fare equation represents the base amount Jeremiah pays for the taxi to pick him up, regardless of distance traveled. It ensures that he incurs a cost even if he does not drive any miles. Therefore, the constant is a starting fee for using the taxi service.
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