Worksheets — Set 19
Optimization & linear programming · Nonlinear optimization
Print and write your answers. Use diagrams to show thinking.
Warm-up
1. Model population P(t) = 300e^{0.22t}. Find P(25). ___ 2. Solve the IVP dy/dt = 22y, y(0) = 23 ___ 3. Optimize: fence a rectangle with perimeter 60. Max area? ___
_See printable PDF for diagram._
Written practice
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? ___ 4. Set up but do not solve: mixing 29% and 49% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 320e^{0.24t}. Find P(27). ___ 8. Solve the IVP dy/dt = 24y, y(0) = 25 ___
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More written practice
1. Optimize: fence a rectangle with perimeter 64. Max area? ___ 2. Set up but do not solve: mixing 32% and 52% solutions = ___ 3. Model population P(t) = 350e^{0.27t}. Find P(30). ___ 4. Solve the IVP dy/dt = 27y, y(0) = 28 ___ 5. Optimize: fence a rectangle with perimeter 70. Max area? ___ 6. Set up but do not solve: mixing 35% and 55% solutions = ___
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Patterns and rules
1. Model population P(t) = 460e^{0.38t}. Find P(41). ___ 2. Solve the IVP dy/dt = 38y, y(0) = 39 ___ 3. Optimize: fence a rectangle with perimeter 92. Max area? ___
_See printable PDF for diagram._
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Stretch
1. Model population P(t) = 540e^{0.46t}. Find P(49). ___ 2. Solve the IVP dy/dt = 46y, y(0) = 47 ___
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Parent tip: Define variables with units