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The problem of growth and decay is stated as follows: The rate of change of a...

The problem of growth and decay is stated as follows: The rate of change of a quantity is proportional to the quantity. The differential equation for such a problem is dy/dt = ±ky.The solution of this growth and decay problem is y(t) = y0e^±kt. Use this solution to answer the following questions if forty percent of a radioactive substance disappears in 100 years. (Use differential equations to solve)

a. What is the half-life of the substance?

b. After how many years will 90% be gone?

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