Functional Modeling Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
A taxi charges \2.50basefareplus base fare plus \0.400.40 per 14\frac{1}{4} mile. Write a cost function C(m)C(m) in terms of miles mm and find the cost of a 66-mile ride.

Solution

  1. 1
    Rate per mile: 0.40 \times 4 = \1.60/mile.So/mile. So C(m)=2.50+1.60m$.
  2. 2
    C(6)=2.50+1.60(6)=2.50+9.60=\12.10$.

Answer

C(m)=2.50+1.60mC(m)=2.50+1.60m; C(6)=\12.10$
Real-world pricing often involves a fixed charge plus a per-unit rate, yielding a linear function. Converting the quarter-mile rate to a per-mile rate simplifies the formula.

About Functional Modeling

Functional modeling uses functions to represent relationships between real-world quantities โ€” choosing the right function family to capture the observed pattern.

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More Functional Modeling Examples

Example 1 easy

A rectangular garden has perimeter [formula] m. Express the area [formula] as a function of the widt

Example 2 medium

A ball is dropped from a [formula] m building. Using [formula], find: (a) height at [formula] s, (b)

Example 4 hard

A cylindrical can must hold [formula] cmยณ. Express the total surface area [formula] as a function of

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