y=(1 + 1/x)^x\ncomplete the table. round your entries to the nearest thousandth.\n| x | y |\n|----|----|\n|…

y=(1 + 1/x)^x\ncomplete the table. round your entries to the nearest thousandth.\n| x | y |\n|----|----|\n| 1 | 2 |\n| 10 | a |\n| 100 | b |\n| 10,000 | c |\n| 100,000 | d |\n| 1,000,000 | e |\n a≈\n b≈\n c≈\n d≈\n e≈
Answer
Explanation:
Step1: Calculate value of $a$
Substitute $x = 10$ into $y=(1+\frac{1}{x})^x$, so $y=(1 + \frac{1}{10})^{10}=(\frac{11}{10})^{10}\approx2.594$.
Step2: Calculate value of $b$
Substitute $x = 100$ into $y=(1+\frac{1}{x})^x$, so $y=(1+\frac{1}{100})^{100}=(\frac{101}{100})^{100}\approx2.705$.
Step3: Calculate value of $c$
Substitute $x = 10000$ into $y=(1+\frac{1}{x})^x$, so $y=(1+\frac{1}{10000})^{10000}\approx2.718$.
Step4: Calculate value of $d$
Substitute $x = 100000$ into $y=(1+\frac{1}{x})^x$, so $y=(1+\frac{1}{100000})^{100000}\approx2.718$.
Step5: Calculate value of $e$
Substitute $x = 1000000$ into $y=(1+\frac{1}{x})^x$, so $y=(1+\frac{1}{1000000})^{1000000}\approx2.718$.
Answer:
$a\approx2.594$ $b\approx2.705$ $c\approx2.718$ $d\approx2.718$ $e\approx2.718$