An earthquake occurs in city P. An expert finds that the magnitude of the earthquake (M) on the Richter scale of a place x km from city P is given by M=Ae^-0.007x, where A is a constant. The magnitude of an earthquake in city Q, which is 100 km from city P, is measured to be 4 on the Richter scale.
(a)Find the magnitude of the earthquake in city P on the Richter scale.
(b)Estimate the area of the region centered at P where the magnitude of the earthquake is 7 or above on the Richter scale. (Give your answer correct to the nearest 100 km^2)
- Prof. PhysicsLv 71 十年前最愛解答
a. Put M = 4, x = 100
4 = Ae^(-0.007)(100), A = 8.055
So, the magnitude of earthquake at P = 8.055e^(-0.007x)
b. Put M = 7,
7 = 8.055e^(-0.007x)
Radius of the area, x = 20.05 km
As the seismic wave spread out uniformly, so the area, A
= 1300 km^2 (to the nearest km^2)資料來源： Physics king