7 multiple choice 1 point the amount of fertilizer in tens of pounds produces a crop yield in the thousands…

Explanation:

Step1: Identify the function type

The function $f(x)=- 0.5x^{2}+2x + 1$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-0.5$, $b = 2$ and $c = 1$. Since $a=-0.5<0$, the parabola opens down - ward and has a maximum.

Step2: Find the x - value of the vertex

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substituting $a=-0.5$ and $b = 2$ into the formula: $x=-\frac{2}{2\times(-0.5)}=\frac{-2}{-1}=2$. Since $x$ is in tens of pounds, the amount of fertilizer is $x\times10 = 2\times10=20$ pounds.

Step3: Find the y - value of the vertex

Substitute $x = 2$ into the function $f(x)=-0.5x^{2}+2x + 1$: $f(2)=-0.5\times(2)^{2}+2\times2 + 1=-0.5\times4 + 4+1=-2 + 4+1=3$. Since $y$ is in thousands of pounds, the crop - yield is $y\times1000=3\times1000 = 3000$ pounds.

Answer:

There is a maximum of 3,000 pounds of crop for 20 pounds of fertilizer.