Worksheets — Set 7

Dynamical systems · First-order and planar systems

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

Warm-up

1. Model population P(t) = 180e^{0.1t}. Find P(13). ___ 2. Solve the IVP dy/dt = 10y, y(0) = 11 ___ 3. Optimize: fence a rectangle with perimeter 36. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 170e^{0.09000000000000001t}. Find P(12). ___ 2. Solve the IVP dy/dt = 9y, y(0) = 10 ___ 3. Optimize: fence a rectangle with perimeter 34. Max area? ___ 4. Set up but do not solve: mixing 17% and 37% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 200e^{0.12000000000000001t}. Find P(15). ___ 8. Solve the IVP dy/dt = 12y, y(0) = 13 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 40. Max area? ___ 2. Set up but do not solve: mixing 20% and 40% solutions = ___ 3. Model population P(t) = 230e^{0.15t}. Find P(18). ___ 4. Solve the IVP dy/dt = 15y, y(0) = 16 ___ 5. Optimize: fence a rectangle with perimeter 46. Max area? ___ 6. Set up but do not solve: mixing 23% and 43% solutions = ___

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Patterns and rules

1. Model population P(t) = 340e^{0.26t}. Find P(29). ___ 2. Solve the IVP dy/dt = 26y, y(0) = 27 ___ 3. Optimize: fence a rectangle with perimeter 68. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units