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.)

Question

Aedan Massey

Mathematics

14 January, 14:16

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.)

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Dana Sparks · Answer 1

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)