Question

A radioactive substance decays exponentially. A scientist begins with 190 milligrams of a radioactive substance. After 19 hours, 95 mg of the substance remains. How many milligrams will remain after 36 hours?

Answer 1

Answer:

  51 milligrams

Step-by-step explanation:

Exponential growth or decay can be modeled by the equation ...

  y = a·b^(x/c)

where 'a' is the initial value, 'b' is the "growth factor", and 'c' is the time period over which that growth factor applies. The time period units for 'c' and x need to be the same.

In this problem, we're told the initial value is a = 190 mg, and the value decays to 95 mg in 19 hours. This tells us the "growth factor" is ...

  b = 95/190 = 1/2

  c = 19 hours

Then, for x in hours the remaining amount can be modeled by ...

  y = 190·(1/2)^(x/19)

__

After 36 hours, we have x=36, so the remaining amount is ...

  y = 190·(1/2)^(36/19) ≈ 51.095 . . . . milligrams

About 51 mg will remain after 36 hours.