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IgorC [24]
4 years ago
8

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?
Mathematics
1 answer:
Alexus [3.1K]4 years ago
8 0

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

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