Algebra II : Value of e

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1 : Factorials

What is the value of \(\displaystyle 5!+3\).

Possible Answers:

\(\displaystyle 63\)

\(\displaystyle 123\)

\(\displaystyle 8\)

\(\displaystyle 23\)

None of the other answers.

Correct answer:

\(\displaystyle 123\)

Explanation:

When evaluating a factorial, you multiply the original number by each integer less than it, stopping at 1.

For this problem, this means that

 \(\displaystyle 5! = 5\cdot 4\cdot 3\cdot 2\cdot 1 = 120\).

Then adding 3, we get the answer 123

Example Question #2 : Factorials

Which of the following best represents the approximate value of \(\displaystyle e^3\)?

Possible Answers:

\(\displaystyle 25\)

\(\displaystyle 15\)

\(\displaystyle 20\)

\(\displaystyle 10\)

\(\displaystyle 30\)

Correct answer:

\(\displaystyle 20\)

Explanation:

The value of \(\displaystyle e\) is defined as \(\displaystyle 2.71828\).

To find \(\displaystyle e^3\), simply cube the decimal number.

\(\displaystyle e^3=2.71828\times 2.71828\times 2.71828 = 20.085\)

The closest value of this number is:  \(\displaystyle 20\)

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