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Charra [1.4K]
3 years ago
10

A radioactive substance decays exponentially. A scientist begins (t=0) with 200 milligrams of a radioactive substance, where the

variable t t represents time (in hours). After 24 hours, 100 mg of the substance remain. How many milligrams will remain at t= 37 hours?
Mathematics
1 answer:
Lady_Fox [76]3 years ago
4 0

Answer:

34.35 mg.

Step-by-step explanation:

We have been given that a radioactive substance decays exponentially. A scientist begins (t=0) with 200 milligrams of a radioactive substance, where the variable t represents time (in hours). After 24 hours, 100 mg of the substance remain.

We know that an exponential decay function is in form A(t)=a\cdot b^t, where,

A(t) = Final amount,

a = Initial value,

b = Decay rate,

t = time.

For our problem initial value (a) is 200, final amount is 100 and time is 24.

100=200\cdot b^{24}

Let us solve for b.

\frac{100}{200}=\frac{200\cdot b^{24}}{200}

0.5=b^{24}

b=0.5^{\frac{1}{24}}

So our required function is A(t)=100\times 0.5^{\frac{1}{24}*t}.

Substitute t=37 in above equation:

A(37)=100\times 0.5^{\frac{1}{24}*37}

A(37)=100\times 0.5^{\frac{37}{24}}

A(37)=100\times 0.3434884118645223

A(37)=34.34884118645223

A(37)\approx 34.35

Therefore, 34.35 milligrams of substance will remain after 37 hours.

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