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Interpreting Negative Exponents and Scientific Notation

5.6.6 Interpreting Negative Exponents and Scientific Notation

5.6.6 • Interpreting Negative Exponents and Scientific Notation

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The equation p=5,000·2tp=5,000·2t represents the population of an invasive fish species in a large lake, tt years since 2005, when the fish population in the lake was first surveyed.

1.

What was the population in 2005?

Compare your answer:

5,000, because 5,000·20=5,0005,000·20=5,000.

2.

What is this value of the population in 2005 in scientific notation?

Compare your answer:

5.0×1035.0×103

3.

For this model, what does it mean when tt is –2?

Compare your answer:

It means 2 years before 2005, which is 2003.

4.

For t=−2t=−2, is the fish population more or less than 1,000? How do you know?

Compare your answer:

More than 1,000. For t=−2t=−2 yeilds 5,000·2−2=1,2505,000·2−2=1,250.

5.

Write the value of the fish population when t=−2t=−2 in scientific notation.

Compare your answer:

1.25×1031.25×103