Practice Mathematical Modeling in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

Building a mathematical version of reality to understand and predict.

Example 1

easy
A taxi charges a base fare of \2.50 and \1.20 per kilometre. Write a mathematical model for the total fare F as a function of distance d (km), identify variables, and compute the fare for a 7 km ride.

Example 2

medium
A population of bacteria doubles every hour. If the initial count is P_0 = 500, write a model for the population P(t) after t hours and find P(4).

Example 3

easy
A rectangle has perimeter P and length l. Express the width w as a function of P and l, then find w when P=30 and l=8.

Example 4

medium
A car travels at a constant speed v km/h. Write a model for distance d after t hours. If the car must reach a destination 240 km away in 3 hours, what speed is required?
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