A material decays a a rate of 1.1% per year. If you start with 250 grams of the material, how much will left in 15 years? Round to the nearest whole gram. What equation correctly models the situation?

Question

anonymous · Answer

dx/dt =1.1%, Let $$N _{0}$$ be the initial amount of material = 250g and initial time = $$t _{0}$$ = 0 years,   and final time = $$t _{f}$$ = 15years

so from the above we can see that the decay problem can be modelled by a differential equation, as it is capable of handling quantities that "change over time"

Traditional Differential Equation (DE) that is applied to these class of problems is;
$$dN/dt = -  \lambda\ *N$$

and the solution to the above DE is...

$$N(t) = N _{0}e ^{-\lambda*t}$$

Now you simply substitute appropriately to get the result.

Hopefully this is enough guidance and you find it useful