Question

A taxi cab charges an initial fee of $2 plus an additional $1.50 per mile traveled. Model the total cost of the taxi ride c as a function of the number of miles driven m.

A. C(m) = 2(1.5m)
B. C(m) = m(2 + 1.5)
C. C(m) = 1.5m + 1.5
D. C(m) = 2m + 1.5

Answer 1

The total cost of a taxi ride as a function of miles driven is represented by the linear equation C(m) = 1.5m + 2, where 1.5 is the cost per mile and 2 represents the initial fee. The correct option is not listed in the choices provided, but Option B is the closest once simplified.

Step-by-step explanation:

The question asks us to model the total cost of a taxi ride c as a function of the number of miles driven m. The taxi charges an initial fee of $2 plus an additional $1.50 per mile traveled. This situation can be described by a linear function where the initial fee represents the y-intercept (the starting cost regardless of miles driven) and the additional charge per mile represents the slope (the rate at which costs increase with each additional mile).

The correct model for this situation is C(m) = 1.5m + 2. This is because for every mile driven (m), the cost increases by $1.50 (which is the slope), and the initial fee (y-intercept) is $2, representing the cost when m is zero. Therefore, the correct option is not presented in the choices above. However, the model closest to the correct representation is Option B, C(m) = m(2 + 1.5), once algebraically simplified.