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

Answer:

0.8167

Step-by-step 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

$e^{-k}=\dfrac{15.89}{35.96}$

Take the natural logarithm of both sides

$-k=ln \dfrac{15.89}{35.96}$

-k=-0.8167

k=0.8167

The decay factor from week to week is 0.8167.