Answer:
About 10 minutes.
Step-by-step explanation:
Let's make an equation to model this situation. This is called exponential decay, so we'll need to use an exponent soon. We're starting with 100 grams:
100
It decays (this means subtraction) by 20.5% per minute. With m = minute:
100(1 - .205)^m
And we want to end up with 10 grams remaining:
100(1 - .205)^m = 10
Let's solve for m now!
100(1 - .205)^m = 10
(1 - .205)^m = 10/100
.795^m = .1
log.795(.1) = m
m = 10.037 = about 10 minutes
Using the exponential function, the time take to have 10 grams of the element left is 10 minutes.
Using the expression function :
Plugging the values into the function :
[tex] 10 = 100( {1 - ( 0.205 )}^{t} [/tex]
[tex] 10 = 100( {0.795)}^{t} [/tex]
Divide both sides by 100
[tex] 0.1 = 0.795^{t} [/tex]
Take the log of both sides
t = (-1 ÷ −0.099632)
t = 10.036
t = 10.0 minutes
Therefore, the time taken in other to have 10 grams left is 10 minutes.
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