Definition Of Modeling

Modeling is the process of representing real life situations through equations or inequalities.

Examples of Modeling

Suppose a laboratory prepares a 200-mg of technetium-99m which has a half-life of 6 hours. Its exponential decay can be modeled by the equation y = 200(0.5)^x

Video Examples: Mathematical Modeling

Solved Example on Modeling

Ques: The population of the world(in million) is modeled by the expression 0.75x² + 74.5x + 4600, where x represents the number of years since 1985. Estimate the world population in 1995.

Choices:

A. 4,420 millions
B. 7,420 millions
C. 6,420 millions
D. 5,420 millions
Correct Answer: D

Solution:

Step 1: [Original model.] 0.75x² + 74.5x + 4600
Step 2: [Replace x = 10 in the model.] 0.75(10)² + 74.5(10) + 4600
Step 3: [Simplify.] = (0.75 × 100) + (74.5 × 10) + 4600
Step 4: = 75 + 745 + 4600
Step 5: = 5420
Step 6: So, the world population in 1995 was 5,420 millions.

Real-world Connections

Mathematical models are used in sciences such as biology and physics and in other fields such as economics and sociology

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