Answer:
58.4 atoms
Explanation:
To find the remaining amount of atoms, you need to use the half-life formula:
[tex]A = A_0*(\frac{1}{2})^{\frac{t}{h}[/tex]
In this formula,
-----> A = remaining amount (atoms)
-----> A₀ = initial amount (atoms)
-----> t = time passed (years)
-----> h = half-life (years)
The half-life is the amount of time that needs to pass for the initial amount of a substance to decay by 50% (or 1/2). According to the graph, 50% of the initial substance is left after 5,730 years.
A = ? atoms t = 16,110 years
A₀ = 410 atoms h = 5,730 years
[tex]A = A_0*(\frac{1}{2})^{\frac{t}{h}[/tex] <----- Half-life formula
[tex]A = 410*(\frac{1}{2})^{\frac{16,110}{5,730}[/tex] <----- Insert values
[tex]A = 410*(\frac{1}{2})^{2.81[/tex] <----- Divide 16,110 by 5,730
[tex]A = 410*0.142[/tex] <----- Raise [tex]\frac{1}{2}[/tex] to 2.81
[tex]A = 58.4[/tex] <-----Multiply 410 and 0.142
