Exponential decay - Quiz
  • 1. What kind of differential equation is used to model a retirement fund?
A) dA/dt = input / output
B) dA/dt = input * output
C) dA/dt = input + output
D) dA/dt = input − output
  • 2. What is the primary factor influencing the decay of a retirement fund according to the text?
A) Random market crashes
B) Continuous tax rates
C) Discrete payout amounts
D) Fluctuating inflation rates
  • 3. What is the input factor for the retirement fund model?
A) A discrete tax rate
B) A continuous interest rate
C) A volatile stock index
D) A fixed monthly salary
  • 4. What does glottochronology aim to estimate for a single language?
A) The age of the language
B) The total number of speakers
C) The geographical origin
D) The phonetic complexity
  • 5. What assumption is made in simple glottochronology?
A) A linear extinction rate
B) A constant decay rate
C) A variable growth rate
D) An exponential growth rate
  • 6. What is the main task of a BGP router's routing table?
A) To block unauthorized access
B) To increase internet speed
C) To encrypt data packets
D) To remember packet paths
  • 7. What happens when a BGP path repeatedly changes state?
A) The path stabilizes
B) The path encrypts data
C) The path deletes itself
D) The path flaps
  • 8. What resources are wasted when a BGP path flaps?
A) Network cable length
B) Hard drive space
C) Power supply voltage
D) CPU and RAM
  • 9. What is the primary purpose of route flapping damping?
A) To expand network capacity
B) To encrypt routing information
C) To speed up data transmission
D) To suppress flapping routes
  • 10. How does the weight assigned by route flapping damping behave?
A) It increases linearly with time
B) It decays exponentially with time
C) It remains constant over time
D) It decreases instantly to zero
  • 11. When does a route get suppressed in BGP routing?
A) When its weight reaches a certain limit
B) When the router restarts
C) When the connection is too fast
D) When no data is being sent
  • 12. What does the BGP router broadcast to peer routers during flapping?
A) Useless information
B) Encrypted routing keys
C) Performance optimization logs
D) Cached user data
  • 13. What is the mathematical solution to the exponential decay differential equation?
A) N(t) = λ e-N0t
B) N(t) = N0 eλt
C) N(t) = N0 - λt
D) N(t) = N0 e-λt
  • 14. What does N0 represent in the exponential decay equation?
A) The decay constant.
B) The initial quantity at t = 0.
C) The total number of decayed elements.
D) The time of decay.
  • 15. How is the mean lifetime (τ) related to the decay constant (λ)?
A) τ = λ2
B) τ = 1 / λ
C) τ = λ
D) τ = 1 - λ
  • 16. What is the alternative form of the decay equation using the mean lifetime?
A) N(t) = N0 e-λt
B) N(t) = N0 e-t/τ
C) N(t) = N0 et/τ
D) N(t) = N0 e-τt
  • 17. At time t = τ, to what fraction of its initial value is the population reduced?
A) 1/2
B) e
C) 1/e
D) 1/λ
  • 18. What is the approximate numerical value of 1/e?
A) 0.6321
B) 0.3679
C) 0.7071
D) 0.5000
  • 19. How many half-lives are approximately equal to one mean lifetime?
A) 1.4427
B) 0.6931
C) 2.0000
D) 1.0000
  • 20. What is the term for the time required for a decaying quantity to fall to one-half of its initial value?
A) Median decay
B) Mean lifetime
C) Decay constant
D) Half-life
  • 21. What symbol is commonly used to denote half-life?
A) N(t)
B) λ
C) t1/2
D) τ
  • 22. How is half-life expressed in terms of the decay constant (λ)?
A) λ / ln(2)
B) ln(λ) / 2
C) λ * ln(2)
D) ln(2) / λ
  • 23. What is the relationship between half-life (t1/2) and mean lifetime (τ)?
A) t1/2 = τ - ln(2)
B) t1/2 = τ * ln(2)
C) t1/2 = τ / ln(2)
D) t1/2 = τ + ln(2)
  • 24. What is the mathematical relationship for mean lifetime (τ) using half-life?
A) τ = t1/2 + ln(2)
B) τ = ln(2) / t1/2
C) τ = t1/2 * ln(2)
D) τ = t1/2 / ln(2)
  • 25. If N(t) is discrete, what is the half-life considered to be?
A) Mean life-time
B) Maximum life-time
C) Median life-time
D) Minimum life-time
  • 26. Given the text, what is the half-life of polonium-210?
A) 1.4427 days
B) 200 days
C) 0.6931 days
D) 138 days
  • 27. According to the text, what is the mean lifetime of polonium-210?
A) 138 days
B) 276 days
C) 100 days
D) 200 days
  • 28. According to the text, the notation λ is a remnant of notation for what?
A) A geometric mean
B) A differential operator
C) A probability constant
D) An eigenvalue
  • 29. What mathematical method is used to compute the expected value of the lifetime?
A) Chain rule
B) Integration by parts
C) Linear regression
D) Separation of variables
  • 30. What symbol represents the combined decay constant for multiple processes?
A) λ1
B) τc
C) λc
D) λt
  • 31. The combined mean life for two decay processes is calculated using which mathematical concept?
A) The quadratic mean.
B) The arithmetic mean.
C) The harmonic mean.
D) The geometric mean.
  • 32. What equation is used to solve systems involving decay chains?
A) Beer-Lambert law
B) Newton's law of cooling
C) Law of large numbers
D) Bateman equation
  • 33. What mathematical law governs decay processes when a sample is small?
A) Poisson process
B) Bateman equation
C) Beer-Lambert law
D) Newton's law
  • 34. What type of chemical reaction follows exponential decay?
A) Zero-order reactions
B) Third-order reactions
C) Second-order reactions
D) First-order reactions
  • 35. At what rate does atmospheric pressure decrease with height?
A) 10% per 1000m
B) 5% per 1000m
C) 15% per 1000m
D) 12% per 1000m
  • 36. What law describes the intensity of electromagnetic radiation in an absorbent medium?
A) Poisson process
B) Bateman equation
C) Beer-Lambert law
D) Newton's law of cooling
  • 37. What term is used for the decay product of a radionuclide?
A) Parent isotope
B) Excited atom
C) Alpha particle
D) Radiogenic nuclide
  • 38. Which component exhibits a decline in resistance as temperature increases?
A) Negative Temperature Coefficient Thermistor
B) Inductor
C) Capacitor
D) Resistor
  • 39. Who won an Ig Nobel Prize for studying the exponential decay of beer froth?
A) Harry Bateman
B) August Beer
C) Arnd Leike
D) Isaac Newton
  • 40. In what type of mechanical system does exponential decay occur?
A) Overdamped systems
B) Resonant systems
C) Underdamped systems
D) Vacuum systems
  • 41. What is the primary condition for a process to be considered truly exponential?
A) The sample must be large
B) The medium must be gaseous
C) The voltage must be constant
D) The temperature must be uniform
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