Answer:
1) Function h
interval [3, 5]
rate of change 6
2) Function f
interval [3, 6]
rate of change 8.33
3) Function g
interval [2, 3]
rate of change 9.6
Step-by-step explanation:
we know that
To find the average rate of change, we divide the change in the output value by the change in the input value
the average rate of change is equal to
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
step 1
Find the average rate of change of function h(x) over interval [3,5]
Looking at the third picture (table)
[tex]f(a)=h(3)=4[/tex]
[tex]f(b)=h(5)=16[/tex]
[tex]a=3[/tex]
[tex]b=5[/tex]
Substitute
[tex]\frac{16-4}{5-3}=6[/tex]
step 2
Find the average rate of change of function f(x) over interval [3,6]
Looking at the graph
[tex]f(a)=f(3)=10[/tex]
[tex]f(b)=f(6)=35[/tex]
[tex]a=3[/tex]
[tex]b=6[/tex]
Substitute
[tex]\frac{35-10}{6-3}=8.33[/tex]
step 3
Find the average rate of change of function g(x) over interval [2,3]
we have
[tex]g(x)=\frac{1}{5}(4)^x[/tex]
[tex]f(a)=g(2)=\frac{1}{5}(4)^2=\frac{16}{5}[/tex]
[tex]f(b)=g(3)=\frac{1}{5}(4)^3=\frac{64}{5}[/tex]
[tex]a=2[/tex]
[tex]b=3[/tex]
Substitute
[tex]\frac{\frac{64}{5}-\frac{16}{5}}{3-2}=9.6[/tex]
therefore
In order from least to greatest according to their average rates of change over those intervals
1) Function h
interval [3, 5]
rate of change 6
2) Function f
interval [3, 6]
rate of change 8.33
3) Function g
interval [2, 3]
rate of change 9.6
