Part A Learning Goal: To understand and use exponential decays. Exponential decay occurs when a quantity y is proportional to the number e taken to the power -t/T. The quantity T is known as the time constant. So we say that y equals A times the quantity (e to the power of minus t over T) and write this mathematically as y = Ae-T/T, where A is a constant. SCALING Whenever t increases by one time constant, y decreases by a factor of 1/e. For instance: • At time t = 0, y = A. • Increasing time to t = 7, reduces y to A/e. ⚫ A further increase to t = 2T reduces y by another factor of 1/e to A/e². Generally, we can say: At t = nT, y has the value A/en. LIMITS As t becomes large, y becomes very small and approaches zero. Consider the case when the constant A = 3 and 7 = 4. Plot the graph of y = 3e-t/4 at each available point from t = 0 to t = 10. + * 血 No elements selected 4.0 3.0 y 2.0 1.0 0 2.0 4.0 6.0 8.0 10.0 t

Part A Learning Goal: To understand and use exponential decays. Exponential decay occurs when a quantity y is proportional to the number e taken to the power -t/T. The quantity T is known as the time constant. So we say that y equals A times the quantity (e to the power of minus t over T) and write this mathematically as y = Ae-T/T, where A is a constant. SCALING Whenever t increases by one time constant, y decreases by a factor of 1/e. For instance: • At time t = 0, y = A. • Increasing time to t = 7, reduces y to A/e. ⚫ A further increase to t = 2T reduces y by another factor of 1/e to A/e². Generally, we can say: At t = nT, y has the value A/en. LIMITS As t becomes large, y becomes very small and approaches zero. Consider the case when the constant A = 3 and 7 = 4. Plot the graph of y = 3e-t/4 at each available point from t = 0 to t = 10. + * 血 No elements selected 4.0 3.0 y 2.0 1.0 0 2.0 4.0 6.0 8.0 10.0 t

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 83AP: A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of...

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