find the average rate of change of ( k(x)=5sqrt{x}+8 ) over the interval ( 1,16 ). write your answer as an…

find the average rate of change of ( k(x)=5sqrt{x}+8 ) over the interval ( 1,16 ). write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

find the average rate of change of ( k(x)=5sqrt{x}+8 ) over the interval ( 1,16 ). write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

Answer

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 = 1), (b=16), and (f(x)=5\sqrt{x}+8).

Step2: Calculate (f(1)) and (f(16))

  • For (x = 1): (f(1)=5\sqrt{1}+8=5\times1 + 8=13).
  • For (x = 16): (f(16)=5\sqrt{16}+8=5\times4+8=20 + 8=28).

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

(\frac{f(16)-f(1)}{16 - 1}=\frac{28 - 13}{15}=\frac{15}{15}=1).

Answer:

(1)