Answer:
Part a) The average rate of change is -0.052
part b) The average rate of change is 0.311
Step-by-step explanation:
we have
[tex]y=-0.005x^4+0.05x^3-0.086x^2-0.04x+2.52[/tex]
we know that
the average rate of change is equal to
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Part a) Calculate the average rate of change from year 0 to year 2
In this problem we have
[tex]a=0[/tex]
[tex]b=2[/tex]
[tex]f(a)=f(0)=-0.005(0)^4+0.05(0)^3-0.086(0)^2-0.04(0)+2.52=2.52[/tex]
[tex]f(b)=f(2)=-0.005(2)^4+0.05(2)^3-0.086(2)^2-0.04(2)+2.52=2.416[/tex]
Substitute
[tex]\frac{2.416-2.52}{2-0}=-0.052[/tex]
Part b) Calculate the average rate of change from year 3 to year 6
In this problem we have
[tex]a=3[/tex]
[tex]b=6[/tex]
[tex]f(a)=f(3)=-0.005(3)^4+0.05(3)^3-0.086(3)^2-0.04(3)+2.52=2.571[/tex]
[tex]f(b)=f(6)=-0.005(6)^4+0.05(6)^3-0.086(6)^2-0.04(6)+2.52=3.504[/tex]
Substitute
[tex]\frac{3.504-2.571}{6-3}=-0.311[/tex]
