4.5 Solving Real-Life Problems Involving Function

4.5 Solving Real-Life Problems Involving Function

Functions are widely used to model and solve real-life problems in areas such as finance, transportation and sales. In finance, functions can represent income, expenses, interest or profit over time. In transportation, functions can describe the relationship between distance, speed and time, helping to calculate travel times or fuel consumption. In sales, functions are used to model revenue, cost and profit based on the number of items sold. Solving these problems involves identifying the relevant variables, expressing their relationship as a function or equation and using algebraic methods to find unknown values, make decisions or predict outcomes.

Example 15

Let $E(n) = 1,500n$ is the total earning (in Rs.) function, where $n$ is the number of days. If labourer works 10 days, find his earning. Solution Given that: $E(n) = 1,500n$ If the labourer works for 10 days, his earning will be $E(10) = 1,500 \times 10$ $= \text{Rs. } 15,000$

Example 16

Let $f(x) = 200 + 15x$ is a function of charging taxi fare (in Rs.), where $x$ represents the number of kilometres. Find proposed fare for a distance of 50 km. Solution $f(x) = 200 + 15x$ Required fare = $f(50) = 200 + 15 \times 50$ $= 200 + 750 = \text{Rs. } 950$