Worksheets — Set 2

Dynamical systems · First-order and planar systems

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

Warm-up

1. Model population P(t) = 130e^{0.05t}. Find P(8). ___ 2. Solve the IVP dy/dt = 5y, y(0) = 6 ___ 3. Optimize: fence a rectangle with perimeter 26. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 120e^{0.04t}. Find P(7). ___ 2. Solve the IVP dy/dt = 4y, y(0) = 5 ___ 3. Optimize: fence a rectangle with perimeter 24. Max area? ___ 4. Set up but do not solve: mixing 12% and 32% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 150e^{0.07t}. Find P(10). ___ 8. Solve the IVP dy/dt = 7y, y(0) = 8 ___

___________________________ ___________________________ ___________________________ ___________________________

More written practice

1. Optimize: fence a rectangle with perimeter 30. Max area? ___ 2. Set up but do not solve: mixing 15% and 35% solutions = ___ 3. Model population P(t) = 180e^{0.1t}. Find P(13). ___ 4. Solve the IVP dy/dt = 10y, y(0) = 11 ___ 5. Optimize: fence a rectangle with perimeter 36. Max area? ___ 6. Set up but do not solve: mixing 18% and 38% solutions = ___

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Patterns and rules

1. Model population P(t) = 290e^{0.21t}. Find P(24). ___ 2. Solve the IVP dy/dt = 21y, y(0) = 22 ___ 3. Optimize: fence a rectangle with perimeter 58. Max area? ___

_See printable PDF for diagram._

___________________________ ___________________________ ___________________________ ___________________________

Parent tip: Define variables with units