A radioactive substance decays at a rate proportional to its mass. A particular specimen of the substance is found to have a mass of 25 grams and is decaying at a rate of 0.025 grams per year. There are m grams left after t years. dm (a) Show that a differential equation relating m and t is =-0.001m dt (b) Find the mass of the specimen after 10 years. c) Find how long it will take for the specimen to decay to 5 grams.

A virus has already infected 4 million people in a country before a vaccine becomes available to the public. Once vaccination starts, the number of infected people decreases at a rate that is proportional to the cube of the number of infected people. One month later, there are still 2 million people that are infected. Let p be the number of infected people (in millions) and t be the number of months since vaccination has started. (a) Find a differential equation and initial conditions to model the situation. (b) Solve the differential equation to find pp as a function of t (c) How many people are still infected three months after vaccination starts?

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Please help for c and d.