- Write down the values of these powers:
a.) 1 ^{2}b.) 2 ^{2}c.) 3 ^{2}d.) 4 ^{2}e.) 5 ^{2}f.) 10 ^{2}g.) 100 ^{2}1 4 = 2*2 9 = 3*3 etc. 16 25 100 10000 ^{2}

- Write down the values of these powers:
a.) 1 ^{3}b.) 2 ^{3}c.) 3 ^{3}d.) 4 ^{3}e.) 5 ^{3}f.) 10 ^{3}g.) 100 ^{3}1 8 = 2*2*2 27 = 3*3*3 etc. 64 125 1000 1000000 ^{3}

- Write down the values of these exponents:
a.) 2 ^{1}b.) 2 ^{2}c.) 2 ^{3}d.) 2 ^{4}e.) 10 ^{1}f.) 10 ^{2}g.) 10 ^{3}2 4 = 2*2 8 = 2*2*2 etc. 16 10 100 1000 ^{N}and 10^{N}

- Write down the values of these logs:
a.) log _{2}2b.) log _{2}4c.) log _{2}8d.) log _{2}16e.) log _{10}10f.) log _{10}100g.) log _{10}10001 2 3 4 1 2 3 _{b}x = y means b^{y}= x

- Write down the values of these functions of N for the
specified values of N:
a.) 100N ^{2}, N = 10b.) 0.01N ^{3}, N = 10c.) 100N ^{2}, N = 100d.) 0.01N ^{3}, N = 10010000 = 100 * (10*10) etc. 10 1000000 10000

- Write down the order (Big-O) of these functions of N:
a.) 100N ^{2}b.) 0.01N ^{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}.*order*even though a. has larger*values*at N = 10 and 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 = 10000 (obtained by solving a. = b. for N)

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

O(N), also called*linear*or*first-order*. This code is O(N) because it just has a single loop, so the execution time is proportional to`n`

.

- Write down the order (Big-O) of this code fragment:
for (i = 0; i < n; i++) for (j = i; 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.