Half-Life (See Section 3.2) Thorium-232 has a half-life of...

Half-Life (See Section 3.2) Thorium-232 has a half-life of 14 billion years. Make a table showing the half-life decay of a sample of thorium-232 from 16 grams to 1 gram; list the time (in years, starting with $t=0$ ) in the first column and the mass (in grams) in the second column. Which type of sequence is each column of the table?

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Key Concepts

Half-Life

Half-life is the period required for a quantity undergoing exponential decay to reduce to half its initial value. It is commonly used in nuclear physics and chemistry to describe the decay of radioactive substances, and it underpins the exponential decay model where, after each half-life period, the remaining substance is halved.

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between any two successive members is constant. In many contexts, such as time intervals measured in equal steps, this sequence type helps represent uniform additive changes where each term increases by a fixed amount relative to the previous term.

Geometric Sequence

A geometric sequence is a sequence of numbers where each term is derived by multiplying the previous term by a constant factor, known as the common ratio. This sequence type is integral to modeling exponential decay processes, where quantities decrease multiplicatively over equal intervals of time.

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