Question

A sample of radioactive element follows the law of exponential decay. if there are 50g of the element at noon 30g at 3:00 pm that same day then how many grams will there be at 9:00 pm that same day?​

Answer 1

10.8 g

Explanation:

Exponential decay equation:
`A=A_0e^(-rt)`

`A_0` is the initial amount (at time t = 0, "noon")

r is the decay rate

You have two pieces of information:

Noon t = 0
`A_0=50`

3:00 pm t = 3
`A=30`

Plug those in to get
`30=50e^(-r(3))`

Divide by 50.

`0.6=e^(-3r)`

Take the natural log of both sides.

`\ln(0.6)=-3r`

Divide by -3.

`(ln((0.6)))/(-3)=r\\\\r \approx .17027`

Now, for 9:00 pm, use this value of r and t = 9.

`A=50e^(-.17027(9)) \approx 10.8`