Question

URGENT PLEASE HELP IM BEGGING YOU

In this activity, you will find and interpret the average rate of change of a polynomial function.

Part A

The polynomial function y = -0.00584 +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.

Answer 1

The average rate of change from year 0 to year 2 is

`change = -0.0585`

The average rate of change from year 3 to year 6 is

`change = -0.0129`

Explanation:

The average rate of change describes the average rate at which gas price in dollars per gallon is changing with respect to time (years)

The given polynomial function is

`y = -0.0058x^4 +0.05x^3 -0.086x^2 - 0.04x + 2.52`

Calculate the average rate of change from year 0 to year 2.

For year x = 0

`y = -0.0058(0)^4 +0.05(0)^3 -0.086(0)^2 - 0.04(0) + 2.52 \\\\y = 2.52`

For year x = 2

`y = -0.0058(2)^4 +0.05(2)^3 -0.086(2)^2 - 0.04(2) + 2.52 \\\\y = -0.0928 + 0.4 - 0.344 - 0.08 + 2.52 \\\\y = 2.403`

The average rate of change from year 0 to year 2 is

`change = (y(2) - y(0))/(x(2) - x(0)) \\\\change = ( 2.403- 2.52)/(2 - 0) \\\\change = (-0.117)/(2) \\\\change = -0.0585`

The negative sign indicates that the gas price has decreased from year 0 to year 2.

The average rate of change from year 3 to year 6 is

For year x = 3

`y = -0.0058(3)^4 +0.05(3)^3 -0.086(3)^2 - 0.04(3) + 2.52 \\\\y = -0.4698 + 1.35 - 0.774 - 0.12 + 2.52 \\\\y = 2.506`

For year x = 6

`y = -0.0058(6)^4 +0.05(6)^3 -0.086(6)^2 - 0.04(6) + 2.52 \\\\y = -7.5168 + 10.8 - 3.096 - 0.24 + 2.52 \\\\ y = 2.4672`

The average rate of change from year 3 to year 6 is

`change = (y(6) - y(3))/(x(6) - x(3)) \\\\change = ( 2.4672- 2.506)/(6 - 3) \\\\change = (-0.0388)/(3) \\\\change = -0.0129`

The negative sign indicates that the gas price has decreased from year 0 to year 2.