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Mathematics Worksheet
🗺️ Mathematical Modeling
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Translate a real situation into a mathematical model.Evaluate linear and exponential models.Follow the five steps of the modeling process.Judge when a model type is appropriate.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1C(x) = 200 + 15x. The cost of 30 units is:
2P(t) = 1000·(1.05)t. The population at t = 2 is:
3A quantity growing by a constant multiple each period suits a:
4The first step of the modeling process is to:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5C(x) = 200 + 15x at x = 30 gives .
6P(t) = 1000(1.05)t at t = 2 gives .
7A cost model is C(x) = 200 + 15x. Find the cost of 30 units.
8A population model is P(t) = 1000·(1.05)t. Find the population at t = 2.
9What are the five general steps of the modeling process?
🚀 Section C · Challenge ● CHALLENGE 5
10Why might a linear model be inappropriate for long-term population growth?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-A 2-A 3-B 4-B | 5 650 6 1102.5 7 = 650 8 = 1102.5 9 = Identify variables, make assumptions, build equations, solve/interpret, validate and refine | 10 = Populations grow multiplicatively (exponentially), not by a constant amount