Algebra 2
Modelling with functions
Making predictions from a model
20 practice questions
0 video lessons
Theory + worked examples
Making Predictions from a Model
California Algebra 2 • Standard F-LE.5 • Modelling with Functions
Making Predictions from a Model is a topic in Modelling with Functions in the California Common Core State Standards. It is aligned to Standard F-LE.5, which requires students to interpret the parameters of a model in context and use it to make predictions.
A model predicts by substituting an input or solving for one; interpolation inside the data is safer than extrapolation outside it.
Theory
A model lets you predict:
- Substitute an \(x\)-value to predict \(y\).
- Solve for \(x\) to predict when \(y\) reaches a value.
- Interpolation (inside the data) is more reliable than extrapolation (outside).
Predictions far outside the data assume the pattern holds — treat them with caution.
Interpolating inside vs extrapolating outside the data.
Ways to predict with a model.
Predict a value or a time:
\[y=f(x)\ \text{(predict } y),\qquad f(x)=y\ \text{(solve for } x)\]
State units and check the prediction is reasonable.
How to predict
- Identify the model.
- To find \(y\), substitute the \(x\)-value.
- To find when, set the model equal and solve.
- Judge whether the answer is reasonable.
Example 1 — Predict a value
A model \(y=2x+3\) fits sales. Predict \(y\) at \(x=6\).
Solution
Substitute \(x=6\).
| \(y\) | \(=\) | \(2(6)+3\) |
| \(=\) | \(15\) |
Example 2 — Predict when
Using \(y=2x+3\), when does \(y=25\)?
Solution
Solve for \(x\).
| \(25\) | \(=\) | \(2x+3\) |
| \(x\) | \(=\) | \(11\) |
Example 3 — Exponential prediction
A population \(P=100(1.2)^t\). Predict \(P\) at \(t=3\).
Solution
Substitute \(t=3\).
| \(P\) | \(=\) | \(100(1.2)^3\) |
| \(\approx\) | \(172.8\) |
Example 4 — Interpolate vs extrapolate
Why is predicting far outside the data risky?
Solution
Extrapolation assumes the pattern continues, which may fail far from the data; interpolation inside the range is safer.
Common pitfalls
Extrapolation is uncertain — the pattern may not continue.
Solve, don't just substitute, to predict a time.
Check reasonableness and units.
Frequently asked questions
How do you predict a value from a model?
Substitute the input into the model.
How do you predict when something happens?
Set the model equal to the target value and solve.
What is the difference between interpolation and extrapolation?
Interpolation predicts inside the data; extrapolation predicts outside it.
Why is extrapolation risky?
The pattern may not hold far from the observed data.
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