Question

A toxic radioactive substance with a density of 2 milligrams per square centimeter is detected in the ventilatingducts of a nuclear processing building that was used 47 years ago. If the half-life of the substance is 20 years,what was the density of the substance when it was deposited 47 years ago? round to the nearest tenth.

Answer 1

The equation for calculating exponential decay is expressed as

A = Aox^t/T

where

A is the final amount after t years

Ao is the initial amount

x is the rate of change

t is the number of years

T is the time taken to achieve the change.

From the information given,

A = 2

t = 47 years

x = 1/2 = 0.5

T = 20

We want to find Ao

By substituting these values into the formula,

2 = Ao(0.5)^(47/20)

2 = Ao(0.5)^2.35

Dividing both sides by (0.5)^2.35, we have

Ao = 2/(0.5)^2.35

Ao = 10.2

the density of the substance when it was deposited 47 years ago is 10.2 milligrams per square centimeter