Answer:
0.50 kg of the material would be left after 10 days.
0.25 kg of the material would be left after 20 days.
Step-by-step explanation:
We have been given that the half-life of a material is 10 days. You have one 1 kg of the material today. We are asked to find the amount of material left after 10 days and 20 days, respectively.
We will use half life formula.
[tex]A=a\cdot(\frac{1}{2})^{\frac{t}{h}}[/tex], where,
A = Amount left after t units of time,
a = Initial amount,
t = Time,
h = Half-life.
[tex]A=1\text{ kg}\cdot(\frac{1}{2})^{\frac{10}{10}}[/tex]
[tex]A=1\text{ kg}\cdot(\frac{1}{2})^{1}[/tex]
[tex]A=1\text{ kg}\cdot\frac{1}{2}[/tex]
[tex]A=0.5\text{ kg}[/tex]
Therefore, amount of the material left after 10 days would be 0.5 kg.
[tex]A=1\text{ kg}\cdot(\frac{1}{2})^{\frac{20}{10}}[/tex]
[tex]A=1\text{ kg}\cdot(\frac{1}{2})^{2}[/tex]
[tex]A=1\text{ kg}\cdot\frac{1^2}{2^2}[/tex]
[tex]A=1\text{ kg}\cdot\frac{1}{4}[/tex]
[tex]A=0.25\text{ kg}[/tex]
Therefore, amount of the material left after 20 days would be 0.25 kg.
