Worksheets — Set 5

Engineering mathematics · Vector calculus

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

Warm-up

1. Model population P(t) = 160e^{0.08t}. Find P(11). ___ 2. Solve the IVP dy/dt = 8y, y(0) = 9 ___ 3. Optimize: fence a rectangle with perimeter 32. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 150e^{0.07t}. Find P(10). ___ 2. Solve the IVP dy/dt = 7y, y(0) = 8 ___ 3. Optimize: fence a rectangle with perimeter 30. Max area? ___ 4. Set up but do not solve: mixing 15% and 35% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 180e^{0.1t}. Find P(13). ___ 8. Solve the IVP dy/dt = 10y, y(0) = 11 ___

___________________________ ___________________________ ___________________________ ___________________________

More written practice

1. Optimize: fence a rectangle with perimeter 36. Max area? ___ 2. Set up but do not solve: mixing 18% and 38% solutions = ___ 3. Model population P(t) = 210e^{0.13t}. Find P(16). ___ 4. Solve the IVP dy/dt = 13y, y(0) = 14 ___ 5. Optimize: fence a rectangle with perimeter 42. Max area? ___ 6. Set up but do not solve: mixing 21% and 41% solutions = ___

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Patterns and rules

1. Model population P(t) = 320e^{0.24t}. Find P(27). ___ 2. Solve the IVP dy/dt = 24y, y(0) = 25 ___ 3. Optimize: fence a rectangle with perimeter 64. Max area? ___

_See printable PDF for diagram._

___________________________ ___________________________ ___________________________ ___________________________

Parent tip: Define variables with units