The half-life of a certain substance is 26 years. How long will it take for a sample of this substance to decay to 92% of its
original amount? Use the exponential decay model, A = A_0 e kt, to solve. years (Round to one decimal place as needed.)
1 answer:
Answer:
t= 3.1 years
Step-by-step explanation:
A = A_0 e kt
Half life(1/2) = 26 yrs
1/2 = 1_0 e^k.26
ln(1/2) = ln(e^26k)
26k. ln(e) = ln(1/2)
k = 1/26* ln(1/2)
k = -0.0267
A = A_0 e^kt
0.92 = 1.e^(-0.0267)t
ln(0.92) = ln(e^(-0.0267)t
-0.0267t .ln(e) = ln(0.92)
t = ln(0.92) / -0.0267
t = 3.122
t = 3.1years (approximate to 1 d.p)
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