Worksheets — Set 17
Differential equations · Laplace transforms and systems
Print and write your answers. Use diagrams to show thinking.
Warm-up
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? ___
_See printable PDF for diagram._
Written practice
1. Model population P(t) = 270e^{0.19t}. Find P(22). ___ 2. Solve the IVP dy/dt = 19y, y(0) = 20 ___ 3. Optimize: fence a rectangle with perimeter 54. Max area? ___ 4. Set up but do not solve: mixing 27% and 47% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 300e^{0.22t}. Find P(25). ___ 8. Solve the IVP dy/dt = 22y, y(0) = 23 ___
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More written practice
1. Optimize: fence a rectangle with perimeter 60. Max area? ___ 2. Set up but do not solve: mixing 30% and 50% solutions = ___ 3. Model population P(t) = 330e^{0.25t}. Find P(28). ___ 4. Solve the IVP dy/dt = 25y, y(0) = 26 ___ 5. Optimize: fence a rectangle with perimeter 66. Max area? ___ 6. Set up but do not solve: mixing 33% and 53% solutions = ___
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Patterns and rules
1. Model population P(t) = 440e^{0.36000000000000004t}. Find P(39). ___ 2. Solve the IVP dy/dt = 36y, y(0) = 37 ___ 3. Optimize: fence a rectangle with perimeter 88. Max area? ___
_See printable PDF for diagram._
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Stretch
1. Model population P(t) = 520e^{0.44t}. Find P(47). ___ 2. Solve the IVP dy/dt = 44y, y(0) = 45 ___
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Parent tip: Define variables with units