Posted by Shreya on .
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,
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,
how do i log both sides? divide by 2000 on both sides?

Pre Calculus 12 
Reiny,
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,
thanks soo much Reiny :) You are such a great math helper on here! :D