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A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 20 hours, 55 mg of the substance remains. How many milligrams will remain after 26 hours

User Cunnel
by
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1 Answer

5 votes

Answer:

44.7 mg

Explanation:

The equation for exponential decay can be written in the form ...

y = a·b^(t/p)

where 'a' is the initial value, 'b' is the decay factor, 'p' is the period over which the decay factor is applicable, and t is time in the same units as p.

Setup

Using the above equation, we have ...

a = initial value = 110 mg

b = decay factor = 55/110 = 1/2 over time period p=20 hours

Then the equation is ...

y = 110·(1/2)^(t/20) . . . . amount remaining after t hours

Solution

We want the amount remaining after 26 hours. That will be ...

y = 110·(1/2)^(26/20) ≈ 44.67

About 44.7 milligrams will remain after 26 hours.

User Manisha Srivastava
by
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