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Real-World Problems in Mathematics: Linear Functions & Modeling

Learn to convert real-world issues into mathematical language and model linear functions for various scenarios like cost, revenue, and depreciation.

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Real-World Problems in Mathematics: Linear Functions & Modeling

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  1. Section 1.3 Linear Functions and Mathematical Modeling

  2. Mathematical Modeling Formulating real world problems into the language of mathematics. Ex. The monthly payment, M, necessary to repay a home loan of P dollars, at a rate of r % per year (compounded monthly), for t years, can be found using

  3. Function A rule that assigns to each value of x one and only one value of y. is a function. Ex. We write f (x) , read “f of x”, in place of y to show the dependency of y on x . So and NOTE: It is notf times x

  4. Linear Function A linear function can be expressed in the form m and b are constants • Can be used for • Simple Depreciation • Linear Supply and Demand Functions • Linear Cost, Revenue, and Profit Functions

  5. Simple Depreciation Ex. A computer with original value $2000 is linearly depreciated to a value of $200 after 4 years. Find an equation for the value, V, of the computer at the end of year t.

  6. Cost, Revenue, and Profit Functions Ex. A shirt producer has a fixed monthly cost of $3600. If each shirt has a cost of $3 and sells for $12 find: a. The cost function Cost: C(x) = 3x + 3600 where x is the number of shirts produced. b. The revenue function Revenue: R(x) = 12x where x is the number of shirts sold. c. The profit from 900 shirts Profit: P(x) = Revenue – Cost = 12x – (3x + 3600) = 9x – 3600 P(900) = 9(900) – 3600 = $4500

  7. Linear Demand Ex. The quantity demanded of a particular game is 5000 games when the unit price is $6. At $10 per unit the quantity demanded drops to 3400 games. Find a demand equation relating the price p, and the quantity demanded, x (in units of 100).

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