Question 1201597
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Answer:  <font color=red size=4>15600 years old</font> (approximate)



Work Shown:


a = starting amount = doesn't matter since it cancels out later
0.15a = 15% of the starting amount


x = number of years
y = amount of material remaining
H = 5700 = half-life


Half-life formula
y = a*(0.5)^(x/H)
0.15a = a*(0.5)^(x/5700)
0.15 = (0.5)^(x/5700)
Log(0.15) = Log( (0.5)^(x/5700) )
Log(0.15) = (x/5700)*Log(0.5)
x/5700 = Log(0.15)/Log(0.5)
x = 5700*Log(0.15)/Log(0.5)
x = 15600.7038867473
x = 15600


The substance is roughly 15600 years old.
Round this however your teacher instructs.
I decided to round to the nearest hundred.
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