Worksheets — Set 6

Methods of applied mathematics · Integral equations and transforms

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

Warm-up

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? ___

_See printable PDF for diagram._

Written practice

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? ___ 4. Set up but do not solve: mixing 16% and 36% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 190e^{0.11t}. Find P(14). ___ 8. Solve the IVP dy/dt = 11y, y(0) = 12 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 38. Max area? ___ 2. Set up but do not solve: mixing 19% and 39% solutions = ___ 3. Model population P(t) = 220e^{0.13999999999999999t}. Find P(17). ___ 4. Solve the IVP dy/dt = 14y, y(0) = 15 ___ 5. Optimize: fence a rectangle with perimeter 44. Max area? ___ 6. Set up but do not solve: mixing 22% and 42% solutions = ___

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Patterns and rules

1. Model population P(t) = 330e^{0.25t}. Find P(28). ___ 2. Solve the IVP dy/dt = 25y, y(0) = 26 ___ 3. Optimize: fence a rectangle with perimeter 66. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units