The Palermo Technical Impact Hazard Scale P is used to quantify the risk associated with the impact

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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 = log10 PE0.8 0.037

where pis 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 dP/dT, assuming that pi = 2 × 10−5 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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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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