Question

find the average rate of change of ( k(x)=16sqrt{x} ) over the interval ( 18,19 ).
write your answer as an integer, fraction, or decimal rounded to the nearest tenth.
simplify any fractions.

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:

\(1.9\)