Mathematical Modeling Math Example 1

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Example 1

easy
A taxi charges a base fare of \2.50and and \1.201.20 per kilometre. Write a mathematical model for the total fare FF as a function of distance dd (km), identify variables, and compute the fare for a 7 km ride.

Solution

  1. 1
    Identify variables: FF = total fare (\),), d$ = distance (km).
  2. 2
    Model: F(d)=2.50+1.20dF(d) = 2.50 + 1.20d.
  3. 3
    For d=7d = 7: F(7)=2.50+1.20ร—7=2.50+8.40=10.90F(7) = 2.50 + 1.20 \times 7 = 2.50 + 8.40 = 10.90.

Answer

F(d)=2.50+1.20d,F(7)=$10.90F(d) = 2.50 + 1.20d,\quad F(7) = \$10.90
A mathematical model translates a real-world situation into equations. Identifying what changes (variables) and what is fixed (parameters) is the first step in building any model.

About Mathematical Modeling

The process of using mathematical structures โ€” functions, equations, distributions โ€” to represent, analyze, and predict real-world phenomena.

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