Membangun dan Menerapkan Model
Diperkenalkan| English | Makna |
|---|---|
| function model/ˈfʌŋkʃn ˈmɒdl/ | model fungsi |
| regression/rɪˈɡreʃn/ | regresi |
| interpolation/ɪnˌtɜːpəˈleɪʃn/ | interpolasi |
| extrapolation/ekˈstræpəleɪʃn/ | ekstrapolasi |
| parameters/pəˈræmɪtəz/ | parameter |
From data to a formula
- Selecting a model family is only half the job; now you build the actual rule.
- A good model turns a table of measurements into a formula you can compute with.
- Once you have the formula, you can predict values you never measured.
- This is how precalculus becomes a tool for the real world.
Build the model
- A function model 函数模型 is a rule that captures how one quantity depends on another.
- You can build it from a verbal description, a table of values, or a graph.
- "Costs $\$5$ to start plus $\$2$ per item" becomes $C = 5 + 2n$ straight away.
- Match the family to the shape (Lesson 1.13), then pin down the exact numbers.
Regression finds the best fit
- With many scattered points, regression 回归 finds the best-fit line or curve using technology.
- It chooses the model that comes closest to all the data at once.
- The result gives you the numbers in the model rule, ready to use.
- No single point sits on it perfectly — it captures the overall trend.
Garis model — baca tingkat dan nilai mulainya
y = ax + b
Di sini a adalah tingkat perubahan dan b adalah nilai awal. Sesuaikan agar sesuai dengan data, lalu masukkan input untuk membuat prediksi.
Regresi menemukan…
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Regresi menyesuaikan model yang paling dekat dengan semua titik sekaligus — model fit terbaik, menggunakan teknologi.
Interpolate versus extrapolate
- Interpolation 内插 predicts between known data points — usually safe.
- Extrapolation 外推 predicts beyond the data — riskier the further you go.
- A model with no data to lean on can drift far from reality.
- Trust interpolation more than extrapolation, and say which one you used.
Memprediksi nilai antara titik data yang diketahui disebut ____.
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Interpolasi tetap berada di dalam rentang data, sehingga biasanya dapat diandalkan.
Memprediksi jauh di luar rentang data (ekstrapolasi) biasanya…
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Jauh dari data, model tidak memiliki bukti untuk ditumpu, sehingga ekstrapolasi adalah prediksi yang paling berisiko.
Interpret the parameters
- The parameters 参数 (the numbers in the rule) carry real-world meaning.
- In $C = 5 + 2n$, the $5$ is the fixed start-up cost and the $2$ is the cost per item.
- Reading parameters in context turns a formula back into a story about the situation.
- A good answer always says what each number means, with its units.
Model memberikan biaya $= 2x + 1$ (dalam ribuan). Prediksikan biaya saat $x = 10$.
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Substitusi: $2(10) + 1 = 21$ ribu. Memasukkan input ke dalam model adalah cara menerapkannya.
Parameter dari sebuah model (seperti kemiringan) dapat diinterpretasikan dalam konteks situasi nyata.
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Dalam biaya $= 2x + 1$, $2$ adalah biaya per unit dan $1$ adalah biaya awal tetap — makna riil.
Susunlah langkah-langkah menggunakan model secara berurutan.
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Data → sesuaikan → prediksikan → periksa. Pemeriksaan terakhir menangkap model yang telah menyimpang dari realitas.
Extrapolating too far is a classic trap. A linear sales model may predict billions of sales in twenty years — clearly nonsense. Always sanity-check a prediction against the real situation before trusting it.
A phone battery drops from $100\%$ by about $8\%$ per hour.
- Model: $B = 100 - 8h$, a linear function model.
- Interpolate at $h = 3$: $B = 100 - 24 = 76\%$ — inside the data, reliable.
- Extrapolate at $h = 20$: $B = -60\%$ — impossible, so the model has broken down.
Build a function model from words, a table, or a graph, using regression for the best fit. Use it to interpolate (safe, inside the data) or extrapolate (risky, beyond it), interpret its parameters in context, and always check the prediction makes real-world sense.