# Science:Math Exam Resources/Courses/MATH102/December 2019/Question 04 (b)

MATH102 December 2019

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### Question 04 (b)

Remember our fishy friends? The quality of hatching of larvae of cold-water fish depends on the temperature of the water. Each hatch is given a quality ranking from 0 to 10, with 10 being a perfect hatch.

As we saw in OSH and WeBWorK, we can sometimes find a non-linear equation that best fits our data by changing the variables in the non-linear equation to make a linear equation, and then using the formula for line of best fit.

Let ${\displaystyle T>0}$ be the temperature in Celsius, and let ${\displaystyle Q}$ be the hatch quality. You decide to fit a function ${\displaystyle Q(T)=10+a(T-4)^{2}}$ to the data in Columns A and B of the table below, choosing the parameter ${\displaystyle a}$ to make the equation fit the data as well as possible.

In order to find the best value of ${\displaystyle a}$, you will use the data you have to compute appropriate values of ${\displaystyle x}$ and ${\displaystyle y}$, then use our formula for a line of best fit passing through the origin. This is done in the spreadsheet below. An arrow indicates the contents of a cell is copied down its column. The entries in Row 1 are labels.

What should you write in cells C2, D2, E2, and F2?

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