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# The amount of a radioactive substance decreases exponentially, with a decay constant of 3% per month. a. Write a differential equation to express the rate of change. b.Find a general solution to the differential equation from part a. c. If there are 75 g at the start of the decay process, find a particular solution for the differential equation from part a. d.Find the amount left after 10 months.

Solution

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(a) The rate of decrease of amount of radioactive substance is equal to $3\%$ of the current amount.

$\boxed{\color{#c34632}\dfrac{dA}{dt}=-0.03A}$

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