Mr. Blackwood is buying boxes of snack-size bags of crackers to pack in his family's school lunches. The first box costs $9.80 and contains 20 bags. The second box contains 30 bags and costs $13.50.

1. Which box is the better buy?

2. Write a mathematical argument that can be used to defend your solution. (Prove your answer in #1 is correct.)

1. The second box

2. When you find the unit cost or unit rate, you’ll find that box 2‘s unit cost is 4 cents less than box 1’s. While not much, it can add up after a while.

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.

b.

step-by-step explanation: