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:

$y=\frac{y_0}{2}$

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

$\frac{1}{2}=e^{-k(1110)}$

Solve for "k":

$undefined$