Question

A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a radioactive substance. After 29 hours, 75 mg of the substance remains. How many milligrams will remain after 33 hours?

Answer 1

We are given

Scientist begins with 150 milligrams of a radioactive substance

so, $P_0=150$

we can use formula

$P(t)=P_0e^{kt}$

we can plug Po=150

$P(t)=150e^{kt}$

After 29 hours, 75 mg of the substance remains

so, at t=29 , P=75

we can plug it

$75=150e^{k\times 29}$

now, we can solve for k

$e^{k29}=\frac{1}{2}$

now, we can take ln on both sides

$\ln \left(e^{k\times \:29}\right)=\ln \left(\frac{1}{2}\right)$

$k=-\frac{\ln \left(2\right)}{29}$

$k=-0.02390$

now, we can plug it back

and we get

$P(t)=150e^{-0.02390t}$

we can plug t=33

$P(33)=150e^{-0.02390\times 33}$

we get

$P(33)=68.16528mg$..............Answer