A model that describes the exponential decay is:

A(t) = A0*e^(kt),

A0 = the initial quantity

t = 1 year the time

A = (1- 0.062)A0 = 0.938A0 the amount left after time t

k = constant

A(1) = A0*e^(k*1)

A(1) = A0e^k

A(1) = 0.938A0

first we will find k:

0.938A0 = A0e^k

e^k= 0.938

let h = half-life time then we have

A(t) = (1/2)A0

(1/2)A0 = A0*e^(k*h)

e^(k*h) = 1/2

(e^k)^h = 1/2

0.938^h = 0.5

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h = 10.83 years

The half-life of the radioactive substance is 10.83 years.