During a pumpkin launching contest, two pumpkins are launched at the same time. the path of pumpkin a is modeled by the equation h(x) = –0.01x2 0.32x 4. the path of pumpkin b is modeled by the equation h(x) = –0.01x2 0.18x 5. if x represents the distance the pumpkin traveled and h(x) represents height, what does the intersection point of the equations represent? a)the height at which the pumpkins reach the greatest distance. b)the distance at which the pumpkins both hit the ground. c)the starting height at which the pumpkins are launched. d)the distance at which the height of the pumpkins are the same.

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.