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?
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
how do i log both sides? divide by 2000 on both sides?
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.
thanks soo much Reiny :) You are such a great math helper on here! :D
To solve this problem involving logarithms, we can use the following formula:
A = P * (1 - r)^t
Where:
A = Final volume (in decibels)
P = Initial volume (in decibels)
r = Rate of decrease (in decimal form, e.g., 10% = 0.1)
t = Time (in this case, the distance traveled in 5m intervals)
In this problem, we are given that the sound decreases by 10% for every 5m traveled. This means the rate of decrease (r) is 0.1.
We are also given that the initial volume (P) is 2000 decibels and we want to find the distance (t) at which the volume decreases to 20 decibels.
Now, let's solve the problem step by step:
Step 1: Plug in the known values into the formula.
A = 20 (final volume)
P = 2000 (initial volume)
r = 0.1 (rate of decrease)
Step 2: Rearrange the formula to solve for t. Divide both sides of the equation by P and take the logarithm of both sides:
(1 - r)^t = A / P
log((1 - r)^t) = log(A / P)
t * log(1 - r) = log(A / P)
t = log(A / P) / log(1 - r)
Step 3: Plug in the values and calculate:
t = log(20 / 2000) / log(1 - 0.1)
Step 4: Simplify the logarithms using a calculator:
t = log(0.01) / log(0.9)
t ≈ -2 / -0.0458
t ≈ 43.6
Therefore, it takes approximately 43.6 times 5m intervals for the volume to decrease from 2000 decibels to 20 decibels.