A certain radioactive material has a half-life of 100 days and the amount of material present, x,

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A certain radioactive material has a half-life of 100 days and the amount of material present, x, satisfies

dx/dt = kx

where t is in days and k is constant.

(a) If there are initially 100 g of this material, find x = f(t). Give your answer with 3 significant digit coefficients.

(b) Use your answer from part(a) to find how long (to the nearest day) it takes for 90% of the radioactivity to dissipate.

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