When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of a radioactive isotope initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?I tried this one many times but I can't seem to get the right answer. Can someone show me how to do this?
Accepted Solution
A:
Answer:after 1 hour 642gafter 3 hour 160.6gafter 4 hour 80.3gStep-by-step explanation:Since we don't know ratio between term so we will use radio decay formula instead of geometric.Formula to use:Radioactive Decay F = Ae ^(-kt)where F = amount left after decay A = initial amount k = constant t = time in hoursPlug in the value from the table to find the value of k322 = 1284e^(-k2)322/1284 = e^(-k2)0.25 = e^(-k2)ln(0.25) = ln(e)^-k2ln(0.25) = -k2ln(e)ln(0.25) / ln(e) = -k2-1.386 = -k2k = 1.386/2Again plug in the value to find amount left after 1 hourk = 0.693F = 1284e ^(-1(0.693))F = 1284(0.5)F = 642gAgain plug in the value to find amount left after 3 hourF = 1284e ^(-3(0.693)) = 1284(0.125) = 160.6gAgain plug in the value to find amount left after 4 hourF = 1284e ^(-4(0.693)) = 1284(0.0625) = 80.3g