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
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...
icon
Related questions
Question
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning