24. A radioactive substance decays exponentially. A scientist begins with 110 milligrams

of a radioactive substance. After 31 hours, 55 mg of the substance remains. How

many milligrams will remain after 42 hours?

Firstly set up the equation as so:

R = me^ (-λt)

From the initial conditions:

110 = me^ (-λ*0)

∴ m = 110

From the other piece of information:

55 = 110e^ (-λ*31)

55/110 = e^ (-31λ)

∴ - ln (2) = - 31λ

λ = ln (2) / 31

Therefore:

R = 110e^ (42 * (-ln (2) / 31))

∴ R ≈ 43 mg

(ln (x) is the natural log of x)