Posted by Shreya on Wednesday, January 23, 2013 at 8:23pm.
Solving problems that involve logarithms
the sound at a rock concert decreases by 10% for every 5m travvelled. how far does it take for a volume of 2000 decibels to decrease to 20 decibels?
i don't know what to do for this one
the growth decay formula i got is
A = P(X)^t/n
I don't know what to do. Can someone please explain step by step?

Pre Calculus 12  Reiny, Wednesday, January 23, 2013 at 9:44pm
In your formula, you don't define X, t, and n
but I am guessing it would be
20 = 2000(.9)^(t/5) ,.... ( .9 because if it decreases by 10% it would leave 90% or .9)
.01 = .9^(t/5)
log both sides
log .01 = log .9^(t/5
2 = (t/5) log.9
t/5 = 2/log.9 = 43.70869..
t = 218.54 m

Pre Calculus 12  Shreya, Wednesday, January 23, 2013 at 10:08pm
how do i log both sides? divide by 2000 on both sides?

Pre Calculus 12  Reiny, Wednesday, January 23, 2013 at 10:31pm
I first of all divided both sides by 2000 to get
.01 = .9^(t/5)
then log both sides
log (.01) = log (.9^(t/5) )
taking the log is a mathematical operation just like multiplying, taking square roots or adding
remember, whatever we do to one side, we must do to the other side.

Pre Calculus 12  Shreya, Wednesday, January 23, 2013 at 10:38pm
thanks soo much Reiny :) You are such a great math helper on here! :D
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