Question

Radon gas has a half-life of 3.83 days. If a basement contains 38g of radon gas, how long until 6.8g are present in the basement? Round to the nearest tenth. SHOW WORK

Answer 1

Basic Exponential model is
\[A(t) = A_0e^{kt}\]
Since the half-life is 3.83 days, we have that the rate of decay is
\[k = \frac{\ln\left(\frac{1}{2}\right)}{3.83} \approx -0.181\]
So the model is
\[A(t) = 38e^{-0.181t}\]
Need to solve for t when A(t) = 6.8, thus
\[6.8 = 38e^{-0.181t}\]

Answer 2

trying not to round off too much, we solve the above equation using the following three steps:

(1) Divide both sides by 38
(2) then take the natural log of both sides
(3) divide both sides by -0.181

You should get approximately 9.5 days