## Related questions with answers

Growing Degree Days The number of growing degree days (GDD) is the sum, over all days in a year in which the temperature is above $40^{\circ} \mathrm{F}$, of the amount that the temperature exceeds $40^{\circ} \mathrm{F}$. It can be approximated by

$f(x, y)=\frac{365}{2 \pi} x-\frac{365}{2}(40-y)+\frac{365(40-y)^2}{\pi x}$

where $x$ is the difference in degrees $\mathrm{F}$ between the average temperature in July and the average temperature in January, and $y$ is the average of those two temperatures.

a. The average January temperature in New York City is $32^{\circ} \mathrm{F}$, and the average July temperature is $77^{\circ} \mathrm{F}$. Use the formula above to approximate the number of GDD. Compare this value with the average of 5945 calculated at www. yourweekendview.com/outlook/agriculture/growingdegree-days/USNY0996.

b. For New York City, find the rate of change of the number of GDD with respect to the average of January and July temperatures if the difference between those averages remains constant.

c. For New York City, find the rate of change of the number of GDD with respect to the difference between average January and July temperatures if the average between those remains constant.

d. Find the average January and July temperature for your home town and compute the number of GDD. Then compare with the actual number from the website given in part a.

Solution

Verified### (a)

The average in January is $32$, and the average in July is $77$. The difference between them is

$x = 77-32 = 45$

The average value is

$y = \frac{32+77}{2} = \frac{109}{2} = 54.5$

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