Question

These tables represent an exponential function. Find the average rate ofchange for the interval from x = 8 to x = 9.хyInterval0110 to 13291 to 2Average rateof change2]x36]x318]*3543x3162]*34863272 to 34813 to 44 to 5524367295 to 6O A. 13,122O B. 3O C. 19,683D. 6561

Answer 1

Average rate can be calculated like the slope

`(y2-y1)/(x2-x1)`

where (x2,y2) is a right point yo (x1,y1)

But we need the values of x=8 and x=9

we realize the change between values of y is the last value by 3 then if

`\begin{gathered} 6\longrightarrow729 \\ 7\longrightarrow729*3=2187 \\ 8\longrightarrow2187*3=6561 \\ 9\longrightarrow6561*3=19683 \end{gathered}`

we have the corresponding values for x=8 and x=9

now replace on the formula of the slope using the points (8 , 6561) and (9 , 19683)

where (9 , 19683) is (x2,y2) and (8 , 6561) is (x1,y1)

`\begin{gathered} (19683-6561)/(9-8) \\ \\ (13122)/(1)=13122 \end{gathered}`

the avreage rate of change for the interval 8 to 9 is 13122

We realize the values of the average are multiplied by 3 too, then we can fi