Mark is draining his pool to clean it. at 12: 00 p. m., he started to drain the pool. at 4: 00 p. m., the pool had 11,600 gallons of water. at 7: 00 p. m., the pool had 6,800 gallons of water. if draining the pool is modeled by a linear function, how many gallons of water were initially in the pool? a) 15,600 b) 18,000 c) 19,400 d)21,200

a - base

b - exponent

so,

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.