find the average rate of change of ( k(x)=18sqrt{x - 3} ) over the interval ( 5,13 ).\nwrite your answer as…

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = k(x)) over the interval ([a,b]) is (\frac{k(b)-k(a)}{b - a}). Here, (a = 5), (b=13), and (k(x)=18\sqrt{x - 3}).

Step2: Calculate (k(13)) and (k(5))

• For (x = 13): (k(13)=18\sqrt{13 - 3}=18\sqrt{10}\approx18\times3.162 = 56.916)
• For (x = 5): (k(5)=18\sqrt{5 - 3}=18\sqrt{2}\approx18\times1.414 = 25.452)

Step3: Substitute into the average - rate - of - change formula

(\frac{k(13)-k(5)}{13 - 5}=\frac{18\sqrt{10}-18\sqrt{2}}{8}=\frac{18(\sqrt{10}-\sqrt{2})}{8}) [ \begin{align*} \frac{18(\sqrt{10}-\sqrt{2})}{8}&=\frac{18(3.162 - 1.414)}{8}\ &=\frac{18\times1.748}{8}\ &=\frac{31.464}{8}\ &=3.933 \end{align*} ]

Answer:

(3.9)