- Write down the values of these powers:
a.) 1 ^{2}b.) 2 ^{2}e.) 5 ^{2}f.) 10 ^{2}g.) 1000 ^{2}1 4 = 2*2 25 = 5*5 etc. 100 (hundred) 1000000 (million) ^{2}(squares)

- Write down the values of these powers:
a.) 1 ^{3}b.) 2 ^{3}e.) 5 ^{3}f.) 10 ^{3}g.) 1000 ^{3}1 8 = 2*2*2 125 = 5*5*5 etc. 1000 (thousand) 1000000000 (billion) ^{3}(cubes)

- Write down the values of these exponents:
a.) 2 ^{0}b.) 2 ^{2}c.) 2 ^{8}e.) 10 ^{1}f.) 10 ^{3}g.) 10 ^{6}1 4 256 10 1000 1000000 ^{N}and 10^{N}(exponentials)

- Write down the values of these logs:
a.) log _{2}1b.) log _{2}4c.) log _{2}256e.) log _{10}10f.) log _{10}1000g.) log _{10}10000000 2 8 1 3 6 _{b}x = y means b^{y}= x

- Write down the values of these functions of N for the
specified values of N:
a.) 10N ^{2}, N = 10b.) 0.1N ^{3}, N = 10c.) 10N ^{2}, N = 100d.) 0.1N ^{3}, N = 1001000 = 10 * (10*10) etc. 100 100000 100000

- Write down the order (Big-O) of these functions of N:
a.) 10N ^{2}b.) 0.1N ^{3}c.) Which has the larger order, a. or b. ? O(N ^{2})O(N ^{3})b. has the larger order because N ^{3}is a higher power than N^{2}.d.) Write down a value of N where b. exceeds a. d.) 101, or any value larger than 100 (see 5c. and 5d.) *order*even though a. has larger*values*at N < 100. We say b. has the larger order because the values of b. will exceed values of a. when N becomes sufficiently large. The crossover point where b. begins to exceed a. occurs when N = 100 (obtained by solving a. = b. for N)

- Write down the order (Big-O) of this code fragment:
for (i = 0; i < n; i++) for (j = 0; j < n; j++) sum = sum + a[i]*b[j]

O(N^{2}), also called*squared*or*quadratic*. This code is O(N^{2}) because it has two nested loops, so the execution time is proportional to`n`

squared -- the body of the inner loop is executed (up to)`n`

times each time the body of the outer loop is executed.