Worksheets — Set 15

Differential equations · Laplace transforms and systems

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

Warm-up

1. Model population P(t) = 260e^{0.18t}. Find P(21). ___ 2. Solve the IVP dy/dt = 18y, y(0) = 19 ___ 3. Optimize: fence a rectangle with perimeter 52. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 250e^{0.16999999999999998t}. Find P(20). ___ 2. Solve the IVP dy/dt = 17y, y(0) = 18 ___ 3. Optimize: fence a rectangle with perimeter 50. Max area? ___ 4. Set up but do not solve: mixing 25% and 45% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 280e^{0.19999999999999998t}. Find P(23). ___ 8. Solve the IVP dy/dt = 20y, y(0) = 21 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 56. Max area? ___ 2. Set up but do not solve: mixing 28% and 48% solutions = ___ 3. Model population P(t) = 310e^{0.22999999999999998t}. Find P(26). ___ 4. Solve the IVP dy/dt = 23y, y(0) = 24 ___ 5. Optimize: fence a rectangle with perimeter 62. Max area? ___ 6. Set up but do not solve: mixing 31% and 51% solutions = ___

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Patterns and rules

1. Model population P(t) = 420e^{0.34t}. Find P(37). ___ 2. Solve the IVP dy/dt = 34y, y(0) = 35 ___ 3. Optimize: fence a rectangle with perimeter 84. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units