Phys Sci 11143 Question Help Qf where Q amount of the subat

Phys Sci 11.1.43 Question Help * Qf where Q amount of the subatance at sime t0,r continuous compound rate of A mathematical model for the decay of radioactive substances is given by Q decay, t = time in years, and Q amount of the substance at time t. An isotope has a haif äife of 15 years. What is the continuous compound rate of decay? The continuous compound rate of decay is ra (Type an integer or decimal rounded to four decimal places as needed)

Solution

Q = Qo*e^rt

t = 15 years

Q = Qo/2

Then

Qo/2 = Qo*e^(r*15)

0.5 = e^(15*r)

15*r = -0.693

r = -0.0462 (Minus sign shows decay)

Decay Rate = 4.62%