Practice Functional Modeling in Math

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

Quick Recap

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

Translate a situation into a function, then use math to analyze it.

Example 1

easy
A rectangular garden has perimeter 40 m. Express the area A as a function of the width w, find the domain, and determine the width that maximizes area.

Example 2

medium
A ball is dropped from a 100 m building. Using h(t)=100-4.9t^2, find: (a) height at t=3 s, (b) time to hit the ground, (c) interpret h'(t) at impact.

Example 3

easy
A taxi charges \2.50 base fare plus \0.40 per \frac{1}{4} mile. Write a cost function C(m) in terms of miles m and find the cost of a 6-mile ride.

Example 4

hard
A cylindrical can must hold 500 cm³. Express the total surface area S as a function of radius r, and find the value of r that minimizes material use.
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