What is the limit of $$e^x$$ as x approaches infinity?

The limit is infinity, indicating that the function grows without bound.

What is the natural logarithm?

The natural logarithm, denoted as $$ln(x)$$ , is the logarithm to the base e.

What is the relationship between exponential functions and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other.

What does it mean for a function to be continuous?

A function is continuous if there are no breaks, jumps, or holes in its graph.

What is the significance of the Euler number in compound interest?

The Euler number is used in the formula for continuous compounding, where the amount grows exponentially.

What is the formula for continuous compounding?

The formula is $$A = Pe^{rt}$$ , where A is the amount, P is the principal, r is the rate, and t is time.

Euler number and compounding

Flashcard

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Mathematics

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9th - 12th Grade

•

Practice Problem

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Hard

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CCSS

8.EE.A.1, HSF-IF.C.8B, HSF-LE.A.1A

Standards-aligned

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FLASHCARD QUESTION

Front

What is the Euler number (e)?

Back

The Euler number (e) is a mathematical constant approximately equal to 2.71828, which is the base of the natural logarithm.

FLASHCARD QUESTION

Front

Back

This property allows us to simplify expressions by adding the exponents when multiplying like bases.

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