MATH 一問 ....

(a)
E = a–6bt

When t = 0, E = 500 J
500 = a–6bx0
a = 500

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(b)
E = 500 x 6bt

When t = 2 s, E = 500-200 = 300 J
300 = 500 x 6b(2)
62b = 0.6
log62b = log0.6
2b = (log0.6)/(log6)
b = (log0.6)/(2log6)
b = -0.1425

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(c)
E = 500 x 6-0.1425t

When E = (500 J)/2 = 250 J
250 = 500 x 6-0.1425t
6-0.1425t = 0.5
log6-0.1425t = log0.5
-0.1425t = (log0.5)/(log6)
t = (log0.5)/(-0.1425log6)
t = 2.715 s

Time taken = 2.715 s

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(d)

When E = 1x10-9 J
1x10-9 = 500x6-0.1425t
6-0.1425t = 2x10-12
log6-0.1425t = log(2x10-12)
-0.1425t = log(2x10-12)/(log6)
t = log(2x10-12)/(-0.1425log6)
t = 105.5 s

Time taken = 105.5 s
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