Question

PLEASE HELP

In 8 days the radioactivity of 1 mg of a radioactive element decreases to 4%. What is the half-life of the element in days

Round your answer to the nearest hundredth.

Answer 1

1.72 days

Explanation:

In 8 days the radioactivity of 1 mg of a radioactive element decreases to 4%.

Initial weight of radioactivity is 1 mg

It is decreases by 4%

4% of 1mg = 0.04 mg

A= ab^{t}

`0.04= 1(b)^8`

take 8th root on both sides

b=0.6687

The equation becomes

A= 1(0.6687)^{t}

To find half life of the element we replace A with 0.5

0.5= 1(0.6687)^{t}

take ln on both sides

`ln(0.5)= t ln(0.6687)`

Divide both sides by ln(0.6687)

so t= 1.72244

t= 1.72 days