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Otrada [13]
2 years ago
8

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 tha

t same day then how many grams will there be at 9:00 pm that same day?​
Mathematics
1 answer:
Leona [35]2 years ago
8 0

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")

<em>r</em> 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 <em>r</em> and  t = 9.

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

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