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*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.