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Step-by-step explanation:
s1 = 1200 g
s2 = 1200×2^(-1/22)
s3 = 1200×2^(-2/22)
...
s23 (22 years later) = 1200×2^-22/22 ≈ 1200×2^-1 = 1200/2
sn = 1200×2^(-(n-1)/22)
what is the n, so that the result is 800 g ?
800 = 1200×2^(-(n-1)/22)
800/1200 = 2^(-(n-1)/22)
2/3 = 2^(-(n-1)/22)
log2(2/3) = -(n-1)/22
22×log2(2/3) = -(n - 1) = -n + 1
n = -22×log2(2/3) + 1 = 13.86917502...
since we stared counting with n=1 for the starting quantity, the number of years is truly 1 less than n (s2 is after 1 year, s3 after 2 years ...).
so, we know for n = 13.86917502..., that in fact
12.86917502... ≈ 12.9 years have passed until the mass of the sample reached 800g.