Worksheets — Set 18

Differential equations · Laplace transforms and systems

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

Warm-up

1. Model population P(t) = 290e^{0.21t}. Find P(24). ___ 2. Solve the IVP dy/dt = 21y, y(0) = 22 ___ 3. Optimize: fence a rectangle with perimeter 58. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 280e^{0.19999999999999998t}. Find P(23). ___ 2. Solve the IVP dy/dt = 20y, y(0) = 21 ___ 3. Optimize: fence a rectangle with perimeter 56. Max area? ___ 4. Set up but do not solve: mixing 28% and 48% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 310e^{0.22999999999999998t}. Find P(26). ___ 8. Solve the IVP dy/dt = 23y, y(0) = 24 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 62. Max area? ___ 2. Set up but do not solve: mixing 31% and 51% solutions = ___ 3. Model population P(t) = 340e^{0.26t}. Find P(29). ___ 4. Solve the IVP dy/dt = 26y, y(0) = 27 ___ 5. Optimize: fence a rectangle with perimeter 68. Max area? ___ 6. Set up but do not solve: mixing 34% and 54% solutions = ___

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Patterns and rules

1. Model population P(t) = 450e^{0.37000000000000005t}. Find P(40). ___ 2. Solve the IVP dy/dt = 37y, y(0) = 38 ___ 3. Optimize: fence a rectangle with perimeter 90. Max area? ___

_See printable PDF for diagram._

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Stretch

1. Model population P(t) = 530e^{0.45t}. Find P(48). ___ 2. Solve the IVP dy/dt = 45y, y(0) = 46 ___

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Parent tip: Define variables with units