Q#1: Suppose that you have two different algorithms for solving a problem. To solve a problem of size n, the first algorithm uses exactly n*exp1-[n+2n+3n+4n]/nlne(10) operations and the second algorithm uses exactly n! operations. As n grows, which algorithm uses fewer operations?

The one of -[n+2n+3n+4n]/nlne(10) has fewer operations because the value of n is static.

The one of n! ( factorial ) is factorised up to n∞ hence has infinity operations.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

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step-by-step explanation: