Worksheets — Set 13

Numerical methods for engineers · Numerical calculus

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

Warm-up

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? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 230e^{0.15t}. Find P(18). ___ 2. Solve the IVP dy/dt = 15y, y(0) = 16 ___ 3. Optimize: fence a rectangle with perimeter 46. Max area? ___ 4. Set up but do not solve: mixing 23% and 43% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 260e^{0.18t}. Find P(21). ___ 8. Solve the IVP dy/dt = 18y, y(0) = 19 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 52. Max area? ___ 2. Set up but do not solve: mixing 26% and 46% solutions = ___ 3. Model population P(t) = 290e^{0.21t}. Find P(24). ___ 4. Solve the IVP dy/dt = 21y, y(0) = 22 ___ 5. Optimize: fence a rectangle with perimeter 58. Max area? ___ 6. Set up but do not solve: mixing 29% and 49% solutions = ___

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Patterns and rules

1. Model population P(t) = 400e^{0.32t}. Find P(35). ___ 2. Solve the IVP dy/dt = 32y, y(0) = 33 ___ 3. Optimize: fence a rectangle with perimeter 80. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units