Solution:
Given that;
As a tornado moves, its speed increases, the function is shown below;
[tex]S(d)=93logd+65[/tex]To calculate the average rate of change for the speed of the wind at the centre of a tornado,
a) For the rate of change for the speed of the wind at the centre of a tornado from mile 10 to 100,
Where, d = 10,
[tex]\begin{gathered} S(10)=93\log_{10}\left(10\right)+65 \\ S(10)=93+65=158\text{ miles/hour} \end{gathered}[/tex]Where, d =100
[tex]S(100)=93\log_{10}\left(100\right)+65=2(93)\log_{10}10+65=186+65=251\text{ miles/hour}[/tex]The average rate of change for the speed of the wind at the centre of a tornado will be
[tex]S=251-158=93\text{ miles/hour}[/tex]Hence, the average rate of change for the speed of the wind at the centre of a tornado from mile 10 to 100 is 93 miles/ hour
b) For the rate of change for the speed of the wind at the centre of a tornado from mile 100 to 1000,
Where, d = 100
[tex]S(100)=93\log_{10}100+65=186+65=251\text{ miles/hour}_[/tex]Where, d = 1000,
[tex]S(1000)=93\log_{10}1000+65=3(93)\log_{10}10+65=279+65=344\text{ miles/hour}[/tex]The average rate of change for the speed of the wind at the centre of a tornado will be
[tex]S=344-351=93\text{ miles/hour}[/tex]Hence, the average rate of change for the speed of the wind at the centre of a tornado from mile 100 to 1000 is 93 miles/ hour