The completed table rounded to the nearest thousandth is
a = 2.594
b = 2.705
c = 2.718
d = 2.718
e = 2.718
Given:
[tex]y = ({1 + \frac{1}{x} })^{x} [/tex]
when x = 10
y = (1 + 1/10)^10
= (1 + 0.1)^10
= 1.1^10
= 2.5937424601
Approximately, 2.594
when x = 100
y = (1 + 1/100)^100
y = (1 + 0.01)^100
y = 1.01^100
= 2.70481382942152609326719471080753083367
Approximately, 2.705
when x = 10,000
y = (1 + 1/10,000)^10,000
y = (1 + 0.0001)^10,000
= 1.0001^10,000
Approximately, 2.718
when x = 100,000
y = (1 + 1/100,000)^100,000
= (1 + 0.00001)^100,000
= 1.00001^100,000
Approximately, 2.718
when x = 1,000,000
y = (1 + 1/1,000,000)^1,000,000
= (1 + 0.000001)^1,000,000
= 1.000001^1,000,000
Approximately, 2.718
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