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83. The Palermo Technical Impact Hazard Scale P is used to quantify the risk associated with the impact of an asteroid colliding with the earth: P;E0.8 P = log10 0.037 where p; is the probability of impact, T is the number of years until impact, and E is the energy of impact (in megatons of TNT). The risk is greater than a random event of similar magnitude if P > 0. (a) Calculate d P/dT, assuming that pi = 2 x 10- and E = 2 megatons. (b) Use the derivative to estimate the change in P if T increases from 8 to 9 years.

83. The Palermo Technical Impact Hazard Scale P is used to quantify the risk associated with the impact of an asteroid colliding with the earth: P;E0.8 P = log10 0.037 where p; is the probability of impact, T is the number of years until impact, and E is the energy of impact (in megatons of TNT). The risk is greater than a random event of similar magnitude if P > 0. (a) Calculate d P/dT, assuming that pi = 2 x 10- and E = 2 megatons. (b) Use the derivative to estimate the change in P if T increases from 8 to 9 years.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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83. The Palermo Technical Impact Hazard Scale P is used to quantify the risk associated with the impact of an asteroid colliding with the earth: P;E0.8 P = log10 0.037 where p; is the probability of impact, T is the number of years until impact, and E is the energy of impact (in megatons of TNT). The risk is greater than a random event of similar magnitude if P > 0. (a) Calculate d P/dT, assuming that pi = 2 x 10- and E = 2 megatons. (b) Use the derivative to estimate the change in P if T increases from 8 to 9 years.
Transcribed Image Text:83. The Palermo Technical Impact Hazard Scale P is used to quantify the risk associated with the impact of an asteroid colliding with the earth: P;E0.8 P = log10 0.037 where p; is the probability of impact, T is the number of years until impact, and E is the energy of impact (in megatons of TNT). The risk is greater than a random event of similar magnitude if P > 0. (a) Calculate d P/dT, assuming that pi = 2 x 10- and E = 2 megatons. (b) Use the derivative to estimate the change in P if T increases from 8 to 9 years.
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