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

Answer:

10.8 g

Step-by-step 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.

$\frac{\ln{(0.6)}}{-3}=r\\\\r \approx .17027$

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

$A=50e^{-.17027(9)} \approx 10.8$