Question

20) After 8 hours, half of a 16-gram sample of a radioactive element remains. Find the constant k for this element for t hours, then use y=ne^-kt to write the equation for modeling it’s exponential decay

- please help me

Answer 1

k = 0.086

Explanation:

We have the equation

y=ne^(-kt)

where y is the amount of radioactive material after t hours, n is the initial amount of radioactive material, and k is some constant.

We know the following data:

• t: 8 hours

• y = n/2 (half of a radioactive element remains)

Replacing into the equation and solving for k:

`y=ne^(-kt)`

`(n)/(2)=ne^(-k8)`

`0.5=e^(-k8)`

`ln(0.5)=ln(e^(-k8))`

`ln(0.5)=-k8ln(e)`

`(ln(0.5))/(-8)=k`

`(ln(0.5))/(-8)=k`

`k = 0.086`