Mathematics: The polynomial function y = -0.005x4 + 0.05x3 – 0.086x2 – 0.04x + 2.52 represents the fluctuating gas price (in dollars per gallon) in a city over the course of 6 years. Calculate the average rate of change from year 0 to year 2, and then calculate the average rate of change from year 3 to year 6.

The polynomial function y = -0.005x4 + 0.05x3 – 0.086x2

rosehayden21

20.01.2022

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

y=-0.005x^4+0.05x^3-0.086x^2-0.04x+2.52

we know that

the average rate of change is equal to

$\frac{f(b)-f(a)}{b-a}$

Part a) Calculate the average rate of change from year 0 to year 2

In this problem we have

a=0

b=2

f(a)=f(0)=-0.005(0)^4+0.05(0)^3-0.086(0)^2-0.04(0)+2.52=2.52

f(b)=f(2)=-0.005(2)^4+0.05(2)^3-0.086(2)^2-0.04(2)+2.52=2.416

Substitute

$\frac{2.416-2.52}{2-0}=-0.052$

Part b) Calculate the average rate of change from year 3 to year 6

In this problem we have

a=3

b=6

f(a)=f(3)=-0.005(3)^4+0.05(3)^3-0.086(3)^2-0.04(3)+2.52=2.571

f(b)=f(6)=-0.005(6)^4+0.05(6)^3-0.086(6)^2-0.04(6)+2.52=3.504

Substitute

$\frac{3.504-2.571}{6-3}=-0.311$

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