# maths: differencial equations?

The rate at which a radioactive specimen decays is given by

d𝑁/d𝑡=−𝛼𝑁

where 𝑁 is the number of radioactive particles at time 𝑡 and 𝛼 is a constant. Solve this equation to find an expression for 𝑁 as a function of time given that 𝑁=𝑁0 at 𝑡=0. Hence find the half-life of the specimen i.e. the time taken for the number of radioactive particles to halve.

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