Worksheets — Set 14

Partial differential equations · Separation of variables

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

Warm-up

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? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 240e^{0.16t}. Find P(19). ___ 2. Solve the IVP dy/dt = 16y, y(0) = 17 ___ 3. Optimize: fence a rectangle with perimeter 48. Max area? ___ 4. Set up but do not solve: mixing 24% and 44% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 270e^{0.19t}. Find P(22). ___ 8. Solve the IVP dy/dt = 19y, y(0) = 20 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 54. Max area? ___ 2. Set up but do not solve: mixing 27% and 47% solutions = ___ 3. Model population P(t) = 300e^{0.22t}. Find P(25). ___ 4. Solve the IVP dy/dt = 22y, y(0) = 23 ___ 5. Optimize: fence a rectangle with perimeter 60. Max area? ___ 6. Set up but do not solve: mixing 30% and 50% solutions = ___

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Patterns and rules

1. Model population P(t) = 410e^{0.33t}. Find P(36). ___ 2. Solve the IVP dy/dt = 33y, y(0) = 34 ___ 3. Optimize: fence a rectangle with perimeter 82. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units