Worksheets — Set 8

Mathematical modeling · Deterministic models

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

Warm-up

1. Model population P(t) = 190e^{0.11t}. Find P(14). ___ 2. Solve the IVP dy/dt = 11y, y(0) = 12 ___ 3. Optimize: fence a rectangle with perimeter 38. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 180e^{0.1t}. Find P(13). ___ 2. Solve the IVP dy/dt = 10y, y(0) = 11 ___ 3. Optimize: fence a rectangle with perimeter 36. Max area? ___ 4. Set up but do not solve: mixing 18% and 38% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 210e^{0.13t}. Find P(16). ___ 8. Solve the IVP dy/dt = 13y, y(0) = 14 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 42. Max area? ___ 2. Set up but do not solve: mixing 21% and 41% solutions = ___ 3. Model population P(t) = 240e^{0.16t}. Find P(19). ___ 4. Solve the IVP dy/dt = 16y, y(0) = 17 ___ 5. Optimize: fence a rectangle with perimeter 48. Max area? ___ 6. Set up but do not solve: mixing 24% and 44% solutions = ___

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Patterns and rules

1. Model population P(t) = 350e^{0.27t}. Find P(30). ___ 2. Solve the IVP dy/dt = 27y, y(0) = 28 ___ 3. Optimize: fence a rectangle with perimeter 70. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units