Zachary's cornfields are irrigated in circular regions, Zachary records data on the com production from various irrigated circular regions Radius (ft) Bushels of corn 500 2,705 1,000 10,818 1,500 24,341 2,000 48,273 2,500 67,613 What type of function best models the given data set? A constant B. exponential C. linear D quadratic

D. about 5,000 ft

Step-by-step explanation:

Given the equation: f(x)=0.01x^2+x+0.2f(x)=0.01x

2

+x+0.2

We want to estimate what radius Zachary would need to irrigate 250,000 bushels of corn.

Substituting f(x)=5000, we have

\begin{gathered}250000=0.01x^2+x+0.2\\0.01x^2+x+0.2-250000=0\\0.01x^2+x-249999.8=0\end{gathered}

250000=0.01x

2

+x+0.2

0.01x

2

+x+0.2−250000=0

0.01x

2

+x−249999.8=0

Using the quadratic formula

x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}x=

2a

−b±

b

2

−4ac

\begin{gathered}a=0.01, b=1, c=-249999.8\\x=\dfrac{-1\pm\sqrt{1^2-4(0.01)(-249999.8)} }{2(0.01)}\\=\dfrac{-1\pm\sqrt{1+9999.992} }{0.02}\\=\dfrac{-1\pm\sqrt{10000.992} }{0.02}\\x\approx \dfrac{-1\pm100 }{0.02}\\x\approx \dfrac{-1+100 }{0.02}\: or\:\dfrac{-1-100 }{0.02}x\approx4950\: or\: -5050 \\$Therefore x\approx 5000ft\end{gathered}

The correct option is D

7

step-by-step explanation: