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 88CP: The first atomic bomb was detonated on July 16, 1945, at the Trinity test site about 200 mi south of...
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Transcribed Image Text: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
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