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?

after 1 hour 642g

after 3 hour 160.6g

after 4 hour 80.3g

Step-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 hours

Plug in the value from the table to find the value of k

322 = 1284e^(-k2)

322/1284 = e^(-k2)

0.25 = e^(-k2)

ln(0.25) = ln(e)^-k2

ln(0.25) = -k2ln(e)

ln(0.25) / ln(e) = -k2

-1.386 = -k2

k = 1.386/2

Again plug in the value to find amount left after 1 hour

k = 0.693

F = 1284e ^(-1(0.693))

F =  1284(0.5)

F = 642g

Again plug in the value to find amount left after 3 hour

F = 1284e ^(-3(0.693))

  =  1284(0.125)

  = 160.6g

Again plug in the value to find amount left after 4 hour

F = 1284e ^(-4(0.693))

  = 1284(0.0625)

  = 80.3g

b is the final answer! : )