Question

The half-life of an element is 680 years. If a laboratory has 120 grams of this element.

a) Write an equation to represent the amount of this element that remains after t years.
b) how long will it toke before it hos 35 grams of this element left?

Answer 1

A(t) = amount remaining in t years

= A0ekt, where A0 is the initial amount and k is a constant to be determined.

Since A(1690) = (1/2)A0 and A0 = 80,

we have 40 = 80e1690k

1/2 = e1690k

ln(1/2) = 1690k

k = -0.0004

So, A(t) = 80e-0.0004t

Therefore, A(430) = 80e-0.0004(430)

= 80e-0.172

≈ 67.4 g