Question

a farming community collected data on the effect of different amounts of fertilizer, x, in 100 kg/ha, on the yield of carrots, y, in tonnes. The resulting quadratic regression model is y=-0.5x^2 + 1.4x +0.1. Determine the amount of fertilizer needed to produce the maximum yield.

Answer 1

To determine the amount of fertilizer needed to produce the maximum yield, we need to find the vertex of the quadratic equation. The vertex represents the maximum point on the graph of the equation.

The given quadratic regression model is y = -0.5x^2 + 1.4x + 0.1.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a and b are the coefficients of the quadratic equation (ax^2 + bx + c).

In this case, a = -0.5 and b = 1.4. Substituting these values into the formula, we get:

x = -(1.4) / (2 * (-0.5))
x = -1.4 / (-1)
x = 1.4

Therefore, the amount of fertilizer needed to produce the maximum yield is 1.4 kg/ha.