question 7 of 10 the value of which of these expressions is closest to e? a. (1 + 1/14)^14 b. (1 + 1/11)^11…

question 7 of 10 the value of which of these expressions is closest to e? a. (1 + 1/14)^14 b. (1 + 1/11)^11 c. (1 + 1/13)^13 d. (1 + 1/12)^12

question 7 of 10 the value of which of these expressions is closest to e? a. (1 + 1/14)^14 b. (1 + 1/11)^11 c. (1 + 1/13)^13 d. (1 + 1/12)^12

Answer

Explanation:

Step1: Recall the definition of $e$

The number $e$ is defined as $\lim_{n\rightarrow\infty}(1 + \frac{1}{n})^n$. The larger the value of $n$, the closer $(1+\frac{1}{n})^n$ is to $e$.

Step2: Compare the values of $n$ in each option

In option A, $n = 14$; in option B, $n=11$; in option C, $n = 13$; in option D, $n=12$. Since $14>13>12>11$, the expression $(1+\frac{1}{14})^{14}$ is the closest to $e$.

Answer:

A. $(1+\frac{1}{14})^{14}$