Euler's Number Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Using a calculator, compute e2e^2 to four decimal places. Then determine whether e2>7e^2 > 7.

Solution

  1. 1
    Calculate: e2=(2.71828…)2≈7.3891e^2 = (2.71828\ldots)^2 \approx 7.3891.
  2. 2
    Since 7.3891>77.3891 > 7, we confirm e2>7e^2 > 7.

Answer

e2≈7.3891>7e^2 \approx 7.3891 > 7
Computing powers of ee builds intuition for the scale of exponential growth. Since e≈2.718e \approx 2.718, squaring it gives approximately 7.3897.389, which is indeed greater than 77.

About Euler's Number

Euler's number e≈2.71828e \approx 2.71828 is the unique base for which the exponential function exe^x is its own derivative — the natural base for growth and decay.

Learn more about Euler's Number →

More Euler's Number Examples

Example 1 easy

Evaluate [formula] and state what this limit defines.

Example 2 hard

Show that the derivative of [formula] is itself, i.e., [formula], using the limit definition of the

Example 4 medium

A bank offers continuous compounding at an annual rate of [formula]. Using [formula], find how much

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