Bismuth-210 is a radioactive material and therefore decays at a rate proportional to the amount present. A 1024 mg sample of Bismuth-210 decayed to 512 mg in 5 days. Let M(t) be the mass of the of this sample in milligrams t days after the initial sample of 1024 mg began to decay.

1) Set up and solve an differential equation with initial conditions to find a formula for M(t).

2) How many milligrams of Bismuth-210 are there after 10 days?

3) What is the half-life of Bismuth-210 according to this data?

4) How long until only 1 milligram of Bismuth remains?