Answer:
The average rate of change of rainfall in the rainforest between 2nd year and 6th year = 3 inches
Step-by-step explanation:
Given function representing inches of rainfall:
[tex]f(x)=3(x-2)+4[/tex]
To find the average rate of change between the 2nd year and the 6th year.
Solution:
The average rate of change between interval [tex][a,b][/tex] is given as :
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
For the given function we need to find the average rate of change between 2nd year and 6th year. [tex][2,6][/tex]
So, we have:
[tex]f(2)=3(2-2)+4=3(0)+4=4[/tex]
[tex]f(6)=3(6-2)+4=3(4)+4=12+4=16[/tex]
Thus, average rate of change will be:
[tex]\frac{f(6)-f(2)}{6-2}[/tex]
⇒ [tex]\frac{16-4}{6-2}[/tex]
⇒ [tex]\frac{12}{4}[/tex]
⇒ [tex]3[/tex]
Thus, the average rate of change of rainfall in the rainforest between 2nd year and 6th year = 3 inches
