Worksheets — Set 17

Algebra II · Multi-step modeling problems

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. Linear model: slope 20, through (0, 23). Write f(x) = ___ 2. Exponential: f(0)=20, growth factor 3.3. f(x)=___ 3. Which model fits: equal differences or equal ratios? ___

_See printable PDF for diagram._

Written practice

1. Linear model: slope 19, through (0, 22). Write f(x) = ___ 2. Exponential: f(0)=19, growth factor 3.2. f(x)=___ 3. Which model fits: equal differences or equal ratios? ___ 4. Parameter meaning: in f(x)=27(0.8)ˣ, 0.8 represents ___ 5. Predict f(22) from your model: ___ 6. When does the model break down? Explain. ___ 7. Linear model: slope 22, through (0, 25). Write f(x) = ___ 8. Exponential: f(0)=22, growth factor 3.5. f(x)=___

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More written practice

1. Parameter meaning: in f(x)=30(0.8)ˣ, 0.8 represents ___ 2. Predict f(25) from your model: ___ 3. Linear model: slope 25, through (0, 28). Write f(x) = ___ 4. Exponential: f(0)=25, growth factor 3.8000000000000003. f(x)=___ 5. Parameter meaning: in f(x)=33(0.8)ˣ, 0.8 represents ___ 6. Predict f(28) from your model: ___

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Patterns and rules

1. Linear model: slope 36, through (0, 39). Write f(x) = ___ 2. Exponential: f(0)=36, growth factor 4.9. f(x)=___ 3. Which model fits: equal differences or equal ratios? ___

_See printable PDF for diagram._

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Stretch

1. Linear model: slope 44, through (0, 47). Write f(x) = ___ 2. Exponential: f(0)=44, growth factor 5.7. f(x)=___

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Parent tip: Look at differences or ratios in tables