Question

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.)

Answer 1

t= 3.1 years

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)