Worksheets — Set 16
Complex variables for engineers · Conformal mapping and applications
Print and write your answers. Use diagrams to show thinking.
Warm-up
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? ___
_See printable PDF for diagram._
Written practice
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? ___ 4. Set up but do not solve: mixing 26% and 46% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 290e^{0.21t}. Find P(24). ___ 8. Solve the IVP dy/dt = 21y, y(0) = 22 ___
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More written practice
1. Optimize: fence a rectangle with perimeter 58. Max area? ___ 2. Set up but do not solve: mixing 29% and 49% solutions = ___ 3. Model population P(t) = 320e^{0.24t}. Find P(27). ___ 4. Solve the IVP dy/dt = 24y, y(0) = 25 ___ 5. Optimize: fence a rectangle with perimeter 64. Max area? ___ 6. Set up but do not solve: mixing 32% and 52% solutions = ___
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Patterns and rules
1. Model population P(t) = 430e^{0.35000000000000003t}. Find P(38). ___ 2. Solve the IVP dy/dt = 35y, y(0) = 36 ___ 3. Optimize: fence a rectangle with perimeter 86. Max area? ___
_See printable PDF for diagram._
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Stretch
1. Model population P(t) = 510e^{0.43000000000000005t}. Find P(46). ___ 2. Solve the IVP dy/dt = 43y, y(0) = 44 ___
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Parent tip: Define variables with units