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Flight formula for Indian spotted owlets The following table shows the average body mass $m(t)$ (in $g$ ) and average wing chord length $w(t)(\text {in } m m),$ along with the derivatives $m^{\prime}(t)$ and $w^{\prime}(t),$ of $t-$week-old Indian spotted owlets. The flight formula function $f(t)=w(t) / m(t)$ which is the ratio of wing chord length to mass, is used to predict when these fledglings are old enough to fly. The values of $f$ are less than $1,$ but approach 1 as t increases. When $f$ is close to $1,$ the fledglings are capable of flying, which is important for determining when rescued fledglings can be released back into the wild. (Source: ZooKeys, 132,2011 ) $$\begin{array}{lrrrr} t & m(t) & m^{\prime}(t) & w(t) & w^{\prime}(t) \\ \hline 1 & 23.32 & 41.45 & 10.14 & 14.5 \\ 1.5 & 50.59 & 64.94 & 20.13 & 26.17 \\ 2 & 82.83 & 57.95 & 36.7 & 39.86 \\ 2.5 & 105.13 & 31.08 & 58.92 & 47.11 \\ 3 & 115.48 & 12.48 & 81.55 & 41.38 \\ 3.5 & 119.4 & 4.44 & 98.99 & 27.94 \\ 4 & 120.76 & 1.51 & 109.75 & 15.74 \\ 4.5 & 121.22 & 0.51 & 115.5 & 7.99 \\ 5 & 121.37 & 0.17 & 118.34 & 3.85 \\ 5.5 & 121.42 & 0.06 & 119.69 & 1.8 \\ 6 & 121.44 & 0.02 & 120.32 & 0.84 \\ 6.5 & 121.45 & 0.01 & 120.61 & 0.38 \end{array}$$ State the units associated with the following derivatives and state the physical meaning of each derivative. a. $m^{\prime}(t)$ b. $w^{\prime}(t)$
c. $f^{\prime}(t)$


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