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Calculus II (MAT 146) Dr. Day Wednes day October 23, 2013

Calculus II (MAT 146) Dr. Day Wednes day October 23, 2013. DEs : Solutions, Solutions, Solutions (9.1-9.4) Applications Involving Differential Equations Assignments and Announcements. Applications!.

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Calculus II (MAT 146) Dr. Day Wednes day October 23, 2013

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  1. Calculus II (MAT 146)Dr. Day Wednesday October 23, 2013 • DEs: Solutions, Solutions, Solutions (9.1-9.4) • Applications Involving Differential Equations • Assignments and Announcements MAT 146

  2. Applications! Rate of change of a population P, with respect to time t, is proportional to the population itself. MAT 146

  3. Rate of change of the population is proportional to the population itself. Slope Fields Euler’s Method Separable DEs MAT 146

  4. Slope Fields MAT 146

  5. Slope Fields MAT 146

  6. Euler’s Method MAT 146

  7. Separable DEs MAT 146

  8. Applications! The radioactive isotope Carbon-14 exhibits exponential decay. That is, the rate of change of the amount present (A) with respect to time (t) is proportional to the amount present (A). MAT 146

  9. Exponential Decay The radioactive isotope Carbon-14 exhibits exponential decay. That is, the rate of change of the amount present (A) with respect to time (t) is proportional to the amount present (A). Carbon-14 has a half-life of 5730 years Write and solve a differential equation to determine the function A(t) to represent the amount, A, of carbon-14 present, with respect to time (t in years), if we know that 300 grams were present initially. Use A(t) to determine the amount present after 250 years. MAT 146

  10. Applications! MAT 146

  11. Applications! Known information: A= 20° C and (0,95) and (20,70) MAT 146

  12. Applications! MAT 146

  13. Applications! MAT 146

  14. MAT 146

  15. Assignments Assignments and Announcements • WebAssign • Ch 9 T/F Review:due Friday at midnight • Ch 9 Applications:due Monday at midnight • Take-Home Assignment #3 due Monday when class starts We will not meet as a group tomorrow (10/24) and Fri (10/25) this week. You are responsible for working on: • Completing THA#3 • Ongoing WA tasks • Prep for Test #3 MAT 146

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