Question

The half-life of radium-226 is 1590 years. (a) If a sample has a mass of 150 mg, find a function that models the mass that remains after t years.

Answer 1

The function that models the remaining mass of radium-226 after t years is A(t) = 150 * (1/2)^(t/1590).

Step-by-step explanation:

To find a function that models the mass that remains after t years for radium-226, we can use the general formula for exponential decay: A(t) = A0 * (1/2)^(t/h), where A(t) represents the remaining mass at time t, A0 is the initial mass, t is the time in years, and h is the half-life. In this case, the initial mass is 150 mg and the half-life is 1590 years. So the function that models the remaining mass after t years is A(t) = 150 * (1/2)^(t/1590).