In a bad late-night science fiction film, a villain is using a large collection

t=1.4hours

Explanation:

The half life is 1hour

At t=0 he has a mass of 4kg

So he want it to be 1kg, so that his weapon can work.

Applying the exponential function of decay

M=Cexp(-kt)

Where,

M is the mass at any time

C is a constant of integration

k is the rate of decay

Given that it has an half life of 1 hours.

Then k is 1

At t =0 the mass is 4kg

Therefore

4=Cexp(0)

C=4

M=4exp(-kt)

Since rate of decay is 1, then k=1

M=4exp(-t)

We need to find t at M=1kg

1=4exp(-t)

1=4exp(-t)

1/4=exp(-t)

0.25=exp(-t)

Take In of both sides

In(0.25)=-t

-1.3863=-t

Then, t=1.386hour

Then it will take about 1.4 hours to get to 1kg.

Why is this on physics?

Explanation: