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Makovka662 [10]
1 year ago
9

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
Mathematics
1 answer:
SpyIntel [72]1 year ago
4 0

Answer:

  44.7 mg

Step-by-step 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.

<h3>Setup</h3>

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

<h3>Solution</h3>

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.

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