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Pre Calculus 12

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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 -

    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 -

    how do i log both sides? divide by 2000 on both sides?

  • Pre Calculus 12 -

    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 -

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

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