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.

0.8167

Step-by-step explanation:

The exponential decay model is given as:

where A(t) is the present amount, is the initial amount, t is time in weeks and k is the decay factor.

From our problem:

A(t)=15.89kg

t=1 week

Therefore:

Divide both sides by 35.96

Take the natural logarithm of both sides

-k=-0.8167

k=0.8167

The decay factor from week to week is 0.8167.

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%