The decay of a radioactive material may be modeled by assuming that the amount A(t) of material present (in grams) at time t(minutes) decays at a rate proportional to the amount present: that is

dA/dt =-kA

for some positive constant k.

1. Derive an equation for the amount A9t) pressent at time t in terms of the constant k and the amount a(0) present at time=0

2. if A(5)=1/3 A(3), find k

3 At what time t will the amount A(t) be 1/4 A(0)?