Worksheets — Set 10

Engineering mathematics · Multiple integration and vector fields

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

Warm-up

1. Model population P(t) = 210e^{0.13t}. Find P(16). ___ 2. Solve the IVP dy/dt = 13y, y(0) = 14 ___ 3. Optimize: fence a rectangle with perimeter 42. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 200e^{0.12000000000000001t}. Find P(15). ___ 2. Solve the IVP dy/dt = 12y, y(0) = 13 ___ 3. Optimize: fence a rectangle with perimeter 40. Max area? ___ 4. Set up but do not solve: mixing 20% and 40% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 230e^{0.15t}. Find P(18). ___ 8. Solve the IVP dy/dt = 15y, y(0) = 16 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 46. Max area? ___ 2. Set up but do not solve: mixing 23% and 43% solutions = ___ 3. Model population P(t) = 260e^{0.18t}. Find P(21). ___ 4. Solve the IVP dy/dt = 18y, y(0) = 19 ___ 5. Optimize: fence a rectangle with perimeter 52. Max area? ___ 6. Set up but do not solve: mixing 26% and 46% solutions = ___

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Patterns and rules

1. Model population P(t) = 370e^{0.29000000000000004t}. Find P(32). ___ 2. Solve the IVP dy/dt = 29y, y(0) = 30 ___ 3. Optimize: fence a rectangle with perimeter 74. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units