Q: What is the exponential of 1000?

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103

1,000 = 1.0 × 103

5000 = 5 x 1000 & 1000 = 10 x 10 x 10 = 2^3 x 5^3 Hence in exp in exponential form 5^(1) x 2^3 x 5^3 Remember for exponents, when multiplying with a common coefficient, you add the exponents(indices) Hence 2^3 x 5^(1 + 3) = 2^3 x 5^4

A __________ function takes the exponential function's output and returns the exponential function's input.

is the relationship linear or exponential

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103

103

1.000000e+3

1,000 = 1.0 × 103

1,000 = 1.0 × 103

31.62

1.0*103

10 to the 3rd power

100 in exponential notation = 102 (representing 10x10) 1000 = 103 (representing 10x10x10) 5000 = 5 x 103

36.5 is not an exponential expression! Its value is 36.536.5 is not an exponential expression! Its value is 36.536.5 is not an exponential expression! Its value is 36.536.5 is not an exponential expression! Its value is 36.5

Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.

Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.