Question

find the average rate of change of ( k(x)=17sqrt{x}-13 ) over the interval ( 9,15 ).
write your answer as an integer, fraction, or decimal rounded to the nearest tenth.
simplify any fractions.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 9\), \(b=15\), and \(f(x)=17\sqrt{x}-13\).

Step2: Calculate \(f(9)\) and \(f(15)\)

• For \(x = 9\): \(f(9)=17\sqrt{9}-13=17\times3 - 13=51 - 13 = 38\).
• For \(x = 15\): \(f(15)=17\sqrt{15}-13\approx17\times3.87298 - 13=65.84066-13 = 52.84066\).

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

\(\frac{f(15)-f(9)}{15 - 9}=\frac{52.84066 - 38}{6}=\frac{14.84066}{6}\approx2.5\).

Answer:

\(2.5\)