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After 15 yr there will be ? g of a radioactive substance

After 15 yr there will be ? g of a radioactive substance-example-1
User Hectooorr
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1 Answer

11 votes
11 votes

Answer:

After 15 years, there will be 3.150 grams of substance.

Explanation:

Remember that the general exponential function for decay is:


Q(t)=Q_0e^(kt)

Where Q(t) is the quantity after t years, and Qo is the initial quantity.

Since we know that there were 10 grams initially and that after 9 years only 5 grams remain, we can say that:


5=10e^(9k)

Solving for k,


\begin{gathered} 5=10e^(9k) \\ \rightarrow(5)/(10)=e^(9k) \\ \\ \rightarrow0.5=e^(9k)\rightarrow\ln(0.5)=9k \\ \\ \Rightarrow k=(\ln(0.5))/(9) \end{gathered}

This way, we'll have that:


Q(t)=10e^{(\ln(0.5))/(9)t}

We can calculate how much substance is left after 15 years as following:


\begin{gathered} Q(15)=10e^{\frac{\operatorname{\ln}(0.5)}{9}*15} \\ \\ \rightarrow Q(15)=3.150 \end{gathered}

We can conclude that after 15 years, there will be 3.150 grams of substance.

User Vinay Vemula
by
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