Question

An unknown substance weighs 35.96kg when it is first brought to the lab. After a week in the lab, a technician weighs it again and finds it weighs 15.89kg. Assuming the substance is decaying exponentially, calculate the decay factor from week to week.

Answer 1

0.8167

Explanation:

The exponential decay model is given as:

`A(t)=A_oe^(-kt)` where A(t) is the present amount,
`A_o` is the initial amount, t is time in weeks and k is the decay factor.

From our problem:

A(t)=15.89kg

`A_o=35.96kg`

t=1 week

Therefore:

`15.89=35.96e^(-k*1)\\`

Divide both sides by 35.96

`e^(-k)=(15.89)/(35.96)`

Take the natural logarithm of both sides

`-k=ln (15.89)/(35.96)`

-k=-0.8167

k=0.8167

The decay factor from week to week is 0.8167.