Question

Radioactive Decay Beginning with 16 grams of a radioactive element whose half -life is 30 years ,the mass y(in grams) remaining after t years is given by

y=23(1/2)^t/45, t ≥ 0.
How much of the initial mass remains after 150 years?

Answer 1

the equation should be corrected to fit the data of the problem. With the corrected equation a mass of 0.5 grams remains after 150 years

Explanation:

for the mass y( in grams)

y=23* (1/2)^(t/45), t ≥ 0.

the initial mass is at t=0 , then

y= 23 grams → should be 16 grams

half-life from the equation = 45 years → should be 30 years

the correct equation should be

y=16*(1/2)^(t/30), t ≥ 0

then after 150 years → t= 150

y=16*(1/2)^(150/30)= 16*(1/2)^5 = 16/32 = 0.5 grams

then a mass of 0.5 grams remains after 150 years