The Palermo Technical Impact Hazard Scale P is used to quantify the risk associated with the impact of an asteroid colliding with the earth:

where p_i 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 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.

Transcribed Image Text:

P = log10 P₁E0.8 0.037