find the average rate of change of ( k(x)=16sqrt{x} ) over the interval ( 18,19 ).\nwrite your answer as an…

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function (y = k(x)) over the interval ([a,b]) is given by (\frac{k(b)-k(a)}{b - a}). Here, (a = 18), (b=19), and (k(x)=16\sqrt{x}).

Step2: Calculate (k(19)) and (k(18))

• (k(19)=16\sqrt{19}\approx16\times4.359 = 69.744)
• (k(18)=16\sqrt{18}\approx16\times4.243 = 67.888)

Step3: Apply the average - rate - of - change formula

(\frac{k(19)-k(18)}{19 - 18}=\frac{16\sqrt{19}-16\sqrt{18}}{1}) (=16(\sqrt{19}-\sqrt{18})) (\approx16(4.359 - 4.243)) (=16\times0.116) (=1.856)

Answer:

(1.9)