Worksheets — Set 4

Mathematical modeling · Deterministic models

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

Warm-up

1. Model population P(t) = 150e^{0.07t}. Find P(10). ___ 2. Solve the IVP dy/dt = 7y, y(0) = 8 ___ 3. Optimize: fence a rectangle with perimeter 30. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 140e^{0.06t}. Find P(9). ___ 2. Solve the IVP dy/dt = 6y, y(0) = 7 ___ 3. Optimize: fence a rectangle with perimeter 28. Max area? ___ 4. Set up but do not solve: mixing 14% and 34% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 170e^{0.09000000000000001t}. Find P(12). ___ 8. Solve the IVP dy/dt = 9y, y(0) = 10 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 34. Max area? ___ 2. Set up but do not solve: mixing 17% and 37% solutions = ___ 3. Model population P(t) = 200e^{0.12000000000000001t}. Find P(15). ___ 4. Solve the IVP dy/dt = 12y, y(0) = 13 ___ 5. Optimize: fence a rectangle with perimeter 40. Max area? ___ 6. Set up but do not solve: mixing 20% and 40% solutions = ___

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Patterns and rules

1. Model population P(t) = 310e^{0.22999999999999998t}. Find P(26). ___ 2. Solve the IVP dy/dt = 23y, y(0) = 24 ___ 3. Optimize: fence a rectangle with perimeter 62. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units