Answer:
The average rate of change is : [tex]6.3[/tex]
Step-by-step explanation:
The number of car owners is modeled by the function;
[tex]f(t)=1.1t^2-2.5t+1.5[/tex], where t is the different number of years.
The average rate of change of f(t) from t=3 to t=5 is simply the slope of the secant line connecting:
(3, f(3)) and (5,f(5))
Which is given by:
[tex]\frac{f(5)-f(3)}{5-3}[/tex]
Now, we substitute t=3 into the function to get;
[tex]f(3)=1.1(3)^2-2.5(3)+1.5[/tex]
[tex]f(3)=3.9[/tex]
We substitute t=5 into the function to get;
[tex]f(5)=1.1(5)^2-2.5(5)+1.5[/tex]
[tex]f(5)=16.5[/tex]
Therefore the average rate of change is : [tex]\frac{14.5-3.9}{2}=6.3[/tex]
