+318 A 20 gram sample of the radioactive element mathtestium takes 10 years to decrease to 15 grams. Find the half life of mathtestium. (You may use e, ln, or log to express your answer)
THIS IS A TEST QUESTION, can someone please solve this as if you were NOT allowed to use a calculator????
thank you
+129852 15 = 20 e^(k* 10) divide both sides by 20
3/4 = e^(10k) taket the Ln of both sides
Ln (3/4) = Ln e^(10 k) and we can write
Ln (.75) = (10k) * Ln e [ Ln e =1....so....we can ignore this ]
Ln (.75) /= 10k divide both sides by 10
Ln (.75)/10 = k
And we want to know when 10 grams remain....so....
10 = 20e^(t * Ln(.75) / 10 ) divide both sides by 20
.5 = e^(t * Ln (.75)/10 ) using a similar proceedure as above
Ln .5 = t * Ln (.75) / 10 multiply both sides by 10 / Ln (.75) and we get that
10 * Ln (.5) / Ln (.75) = t
This is the exact answer........you will need a calculator from here [ the answer is ≈ 24.09 yrs ]
