Respuesta :
Answer:
The average rate of change from year 0 to year 2 is
[tex]change = -0.0585[/tex]
The average rate of change from year 3 to year 6 is
[tex]change = -0.0129[/tex]
Step-by-step 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
[tex]y = -0.0058x^4 +0.05x^3 -0.086x^2 - 0.04x + 2.52[/tex]
Calculate the average rate of change from year 0 to year 2.
For year x = 0
[tex]y = -0.0058(0)^4 +0.05(0)^3 -0.086(0)^2 - 0.04(0) + 2.52 \\\\y = 2.52[/tex]
For year x = 2
[tex]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[/tex]
The average rate of change from year 0 to year 2 is
[tex]change = \frac{y(2) - y(0)}{x(2) - x(0)} \\\\change = \frac{ 2.403- 2.52}{2 - 0} \\\\change = \frac{-0.117}{2} \\\\change = -0.0585[/tex]
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
[tex]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[/tex]
For year x = 6
[tex]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[/tex]
The average rate of change from year 3 to year 6 is
[tex]change = \frac{y(6) - y(3)}{x(6) - x(3)} \\\\change = \frac{ 2.4672- 2.506}{6 - 3} \\\\change = \frac{-0.0388}{3} \\\\change = -0.0129[/tex]
The negative sign indicates that the gas price has decreased from year 0 to year 2.
