Question

Complete the average rate of change (ARC) for the function H(n) = 5/ n + 1 On the interval [2, 10] ARC[2, 10] = ________

Answer 1

`H(n)=(5)/(n+1)`

Averate rate of change:

`\begin{gathered} \lbrack a,b\rbrack \\ \\ ARC=(H(b)-H(a))/(b-a) \end{gathered}`

For the given interval:

`\begin{gathered} \text{ARC}_(\lbrack2,10\rbrack)=(H(10)-H(2))/(10-2) \\ \\ \text{ARC}_(\lbrack2,10\rbrack)=((5)/(10+1)-(5)/(2+1))/(8) \\ \\ \text{ARC}_(\lbrack2,10\rbrack)=((5)/(11)-(5)/(3))/(8) \\ \\ \text{ARC}_(\lbrack2,10\rbrack)=((15-55)/(33))/(8) \\ \\ \text{ARC}_(\lbrack2,10\rbrack)=(-(40)/(33))/(8) \\ \\ \text{ARC}_(\lbrack2,10\rbrack)=(-40)/(33\cdot8) \\ \\ \text{ARC}_(\lbrack2,10\rbrack)=-(40)/(264) \\ \\ \text{ARC}_(\lbrack2,10\rbrack)=-(5)/(33)=-0.\bar{15} \end{gathered}`

Then, the averate rate of change of the given function in the interval {2,10} is -5/33 (or -0.15)