Question

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

Answer 1

Answer:

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

Step-by-step 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,

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

This way, we'll have that:

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

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

$\begin{gathered} Q(15)=10e^{\frac{\operatorname{\ln}(0.5)}{9}\times15} \\ \\ \rightarrow Q(15)=3.150 \end{gathered}$

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