Question

Element X is a radioactive isotope such that every 42 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 50 grams, how long
would it be until the mass of the sample reached 45 grams, to the nearest tenth of a
year?

Answer 1

Answer:

6.38548 years

Step-by-step explanation:

1 = 2 $e^{42k}$

1/2 =   $e^{42k}$

ln(1/2) = 42k ln(e)

ln(1/2)/42 = k

k = -0.01650

~~~~~~~~~~~~~~

45 = 50 $e^{-0.01650t}$

45/50 =   $e^{-0.01650t}$

ln(45/50) =  -0.01650 t ln(e)

ln(45/50)/ -0.01650 = t

t = 6.38548 years