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Unit 5, Lesson 8

Unknown Exponents

Algebra 2

A pattern of dots grows exponentially. The table shows the number of dots at each step of the pattern.

step number	0	1	2	3
number of dots	1	5	25	125

Write an equation to represent the relationship between the step number, \(n\), and the number of dots, \(y\).
At one step, there are 9,765,625 dots in the pattern. At what step number will that happen? Explain how you know.

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Complete the table.

\(x\)			-2	0	\(\frac{1}{3}\)	1
\(10^x\)	\(\frac{1}{10,000}\)	\(\frac{1}{1,000}\)	\(\frac{1}{100}\)	\(\hspace{.6cm}\)	\(\hspace{.6cm}\)	\(\hspace{.6cm}\)	1,000	1,000,000,000

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The half-life of carbon-14 is about 5730 years.

Complete the table, which shows the amount of carbon-14 remaining in a plant fossil at the different times since the plant died.
About how many years will it be until there is 0.1 picogram of carbon-14 remaining in the fossil? Explain how you know.

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