A radioactive substance decays according to :
$$x' = -ax$$
where $a>0$ is a constant. After $2$ days there are $1,000$ grams and after $7$ days there are $300$ grams. How many grams were there initially?
I'm unsure how I'd go on with doing this, any help would be greatly appreciated...
Cheers.
EDIT: The step I got upto was separation of variables/integration:
$$x = e^{-at}$$
Can you solve the differential equation? You should have a solution with two constants-the initial amount and $a$. The two pieces of data give you two equations in two unknowns to find these constants.
Added: your solution needs a constant of integration. The solution should be $x=c\cdot e^{-at}$. Now plug in the data you are given: $$1000=c\cdot e^{-2a}\\300=c \cdot e^{-7a}$$ Now solve those for $a,c$ and $x(0)$ is just $c$