Question

Tvor om your 4. SPreCalc7 4.6.017. My Notes A This exercise uses the radioactive decay model. The half-life of radium-226 is 1600 years. Suppose we have a 26-mg sample. (a) Find a function m(t)- mo2th that models the mass remaining after t years m(t) - 26.2 (b) Find a function m(t) = moet that models the mass remaining after years. (Round your r value to six decimal places.) m(t) - 26.e-0.0004336 (c) How much of the sample will remain after 3000 years? (Round your answer to one decimal place.) mg d) After how many years will only 15 mg of the sample remain? (Round your answer to one decimal place.) Need Help? Read it Watch It Talk to Tutor Show My Work (Optional

Answer 1

Part c).

k = 1/t ln(m₀/m(t))

i.e. ln(2)/1600 yr = 1/3000 yr * ln(26 mg/m(t))

i.e. m(t) = 7.1 mg

Part d).

ln(2)/1600 yr = 1/t ln(26/15)

i.e. t = 1269.68 years