Answer:
Step-by-step explanation:
We get to use the simple version of the half life equation:
[tex]N=N_0(\frac{1}{2})^{\frac{t}{H}[/tex] where N is the amount of radioactive element left after a specific number of years,
N0 is the initial amount of the element,
t is the number of years (our unknown), and
H is the Half life of the element. For us,
N is 61
N0 is 70,
t is unknown,
H is 24 years. Filling in:
[tex]61=70(.5)^{\frac{t}{24}[/tex]. We begin by dividing both sides by 70 to get:
[tex].8714285=(.5)^{\frac{t}{24}[/tex] and then take the natural log of both sides:
[tex]ln(.8714285=ln(.5)^{\frac{t}{24}[/tex] which allows us to bring down the exponent to the front on the right side:
[tex]ln(.8714285)=\frac{t}{24}ln(.5)[/tex]. We divide both sides by ln(.5) to get:
[tex].1985457976=\frac{t}{24}[/tex] and then multiply both sides by 24 to get:
t = 4.8 years
