Worksheets — Set 20
Partial differential equations · First-order equations and classification
Print and write your answers. Use diagrams to show thinking.
Warm-up
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._
Written practice
1. Model population P(t) = 300e^{0.22t}. Find P(25). ___ 2. Solve the IVP dy/dt = 22y, y(0) = 23 ___ 3. Optimize: fence a rectangle with perimeter 60. Max area? ___ 4. Set up but do not solve: mixing 30% and 50% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 330e^{0.25t}. Find P(28). ___ 8. Solve the IVP dy/dt = 25y, y(0) = 26 ___
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More written practice
1. Optimize: fence a rectangle with perimeter 66. Max area? ___ 2. Set up but do not solve: mixing 33% and 53% solutions = ___ 3. Model population P(t) = 360e^{0.28t}. Find P(31). ___ 4. Solve the IVP dy/dt = 28y, y(0) = 29 ___ 5. Optimize: fence a rectangle with perimeter 72. Max area? ___ 6. Set up but do not solve: mixing 36% and 56% solutions = ___
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Patterns and rules
1. Model population P(t) = 470e^{0.39t}. Find P(42). ___ 2. Solve the IVP dy/dt = 39y, y(0) = 40 ___ 3. Optimize: fence a rectangle with perimeter 94. Max area? ___
_See printable PDF for diagram._
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Stretch
1. Model population P(t) = 550e^{0.47000000000000003t}. Find P(50). ___ 2. Solve the IVP dy/dt = 47y, y(0) = 48 ___
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Parent tip: Define variables with units