Worksheets — Set 12

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) = 230e^{0.15t}. Find P(18). ___ 2. Solve the IVP dy/dt = 15y, y(0) = 16 ___ 3. Optimize: fence a rectangle with perimeter 46. Max area? ___

_See printable PDF for diagram._

Written practice

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? ___ 4. Set up but do not solve: mixing 22% and 42% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 250e^{0.16999999999999998t}. Find P(20). ___ 8. Solve the IVP dy/dt = 17y, y(0) = 18 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 50. Max area? ___ 2. Set up but do not solve: mixing 25% and 45% solutions = ___ 3. Model population P(t) = 280e^{0.19999999999999998t}. Find P(23). ___ 4. Solve the IVP dy/dt = 20y, y(0) = 21 ___ 5. Optimize: fence a rectangle with perimeter 56. Max area? ___ 6. Set up but do not solve: mixing 28% and 48% solutions = ___

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Patterns and rules

1. Model population P(t) = 390e^{0.31t}. Find P(34). ___ 2. Solve the IVP dy/dt = 31y, y(0) = 32 ___ 3. Optimize: fence a rectangle with perimeter 78. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units