Acherry farm estimates from past records that if 23 trees are planted per acre, each tree will yield an average of 55 pounds of cherries per season. if for each additional tree planted per acre the average yield per tree is reduced by 1 pound, how many trees should be planted per acre to obtain the maximum yield per acre.?

  39

Step-by-step explanation:

Yield goes down 1 lb for each tree over 23 per acre, so the yield per tree as a function of x trees per acre is ...

  yield per tree = 55 -(x -23) = 78 -x . . . . . pounds of cherries

To get the yield per acre, we multiply the number of trees per acre by the yield per tree:

  lb/acre = (x tree/acre)((78 -x) lb/tree) = x(78 -x)

This is a quadratic function that opens downward and has zeros at x=0 and x=78. The vertex (maximum) is on the line of symmetry, halfway between the zeros. The yield per acre will be a maximum when ...

  x = (0 +78)/2 = 39 . . . . trees per acre

39 trees should be planted per acre to maximize yield per acre.

there is no grid

step-by-step explanation:

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.