Question

The model for radioactive decay Is y = yoek. A radioactive substance has a half-life of 1110 years. If 50 grams are present today, in how many years will 31 gramsbe present? While solving this problem, round the value of k to seven decimal places. Round your answer to two decimal places.

Answer 1

Given the equation:

`y=y_0e^(-kt)`

You know that the radioactive substance has this half-life (in years)

`t=1110`

And:

`y=(y_0)/(2)`

Therefore, you can rewrite the equation in this form in order to find "k":

`(1)/(2)=e^(-k(1110))`

Solve for "k":