Worksheets — Set 11

Differential equations · Laplace transforms and systems

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

Warm-up

1. Model population P(t) = 220e^{0.13999999999999999t}. Find P(17). ___ 2. Solve the IVP dy/dt = 14y, y(0) = 15 ___ 3. Optimize: fence a rectangle with perimeter 44. Max area? ___

_See printable PDF for diagram._

Written practice

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? ___ 4. Set up but do not solve: mixing 21% and 41% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 240e^{0.16t}. Find P(19). ___ 8. Solve the IVP dy/dt = 16y, y(0) = 17 ___

___________________________ ___________________________ ___________________________ ___________________________

More written practice

1. Optimize: fence a rectangle with perimeter 48. Max area? ___ 2. Set up but do not solve: mixing 24% and 44% solutions = ___ 3. Model population P(t) = 270e^{0.19t}. Find P(22). ___ 4. Solve the IVP dy/dt = 19y, y(0) = 20 ___ 5. Optimize: fence a rectangle with perimeter 54. Max area? ___ 6. Set up but do not solve: mixing 27% and 47% solutions = ___

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Patterns and rules

1. Model population P(t) = 380e^{0.30000000000000004t}. Find P(33). ___ 2. Solve the IVP dy/dt = 30y, y(0) = 31 ___ 3. Optimize: fence a rectangle with perimeter 76. Max area? ___

_See printable PDF for diagram._

___________________________ ___________________________ ___________________________ ___________________________

Parent tip: Define variables with units