Tables
Powers of e

The irrational number e (Greek lower case "e"), approximately 2.718281828459, occurs in many contexts where growth is taking place. Logarithms to the base e (natural logarithms) are often preferred to common logarithms in these contexts, since they provide a more elegant, indeed a more natural, formulation. e may be defined as the limit, as x tends to infinity, of the expression (1 + 1/x)*x.

Growth equations often involve the expression e*x. The point seems to be that the rate of change of this function, at any point x = k, is equal to e*k. Newton in 1665 showed that

e*x = 1 + x + x*2/2! + x*3/3! + x*4/4! + . . .

We give here the first 32 powers of e (that is, the first 32 values of e*x).

Table

 e*0 1.0000000000000 e*1 2.7182818284590 e*2 7.3890560989304 e*3 20.085536923186 e*4 54.598150033138 e*5 148.41315910255 e*6 403.42879349265 e*7 1,096.6331584282 e*8 2,980.9579870409 e*9 8,103.0839275729 e*10 22,026.265794799 e*11 59,874.141715175 e*12 162,754.79141893 e*13 442,413.39200871 e*14 1,202,604.2841641 e*15 3,269,017.3724702 e*16 8,886,110.5205025 e*17 24,154,952.753560 e*18 65,659,969.137287 e*19 178,482,300.96306 e*20 485,165,195.40943 e*21 1,318,815,734.4822 e*22 3,584,912,846.1287 e*23 9,744,803,446.2408 e*24 26,489,122,129.821 e*25 72,004,899,337.323 e*26 195,729,609,428.66 e*27 532,048,240,601.30 e*28 1,446,257,064,290.0 e*29 3,931,334,297,139.9 e*30 10,686,474,581,513. e*31 29,048,849,665,215. e*32 78,962,960,182,591.

See also our separate table for fractional powers of e*x), which is convenient for some Poisson problems.