指數及對數函數－百科全書

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指數及對數函數

發問:

a. 函數y=3^(x-1)的略圖利用該圖像，解不等式：3^x<18 b. 計算在下列各不同震級的地震中所釋放出的能量。(答案準確至三位有效數字。) (i) 黎克特制2級 (ii) 黎克特制3級

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a. 函數y=3^(x-1)的略圖利用該圖像，解不等式：3^x<18 The graph shows that the function is monotonically increasing from -inf, and reaches y=18 at about 3.6. See: http://i263.photobucket.com/albums/ii157/mathmate/math/3_x-1.png Therefore, f(x)=3^x<18 is for all (x-1)<3.6, or x<4.6. More precisely, x<4.6309... = 1+1+log(18)/log(3) b. 計算在下列各不同震級的地震中所釋放出的能量。(答案準確至三位有效數字。) (i) 黎克特制2級 (ii) 黎克特制3級 (i) Intensity 2 on the Richter scale is equaivalent to the detonation of one metric tonne of TNT explosive, and the energy is released is 1 GJ (giga joules, or 10^9 joules). (ii) When the intensity is increased by 2, the energy is increased by 1000 times, which means that for every unit increase in intensity, the energy is increased by 10^(3/2) times, or 31.622 times. Thus for an intensity of 3, the energy released is 1GJ*31.622=31.622 GJ. 2007-12-17 11:27:30 補充：函數y=3^(x-1)的略圖