Helpppppp!! Calculus!

Question

The average retail price of gas in canada from 1979 to 2008,can be medelled by the polynomial function p(x)= 0.008y^2 + 4.830y + 25.720. where P is the price of gas in cents per litre and (y) is the number of Year after 1979.

 

a) Show how to use this equation to determine the price of gas in 1980.

 

b) Show how to use this equation to determine the price of gas in 2000.

 

c) Assume that this equation could be used to determine the price of gas in 2014 although it states that it only valid until 2008. Based on this equation , what should the price of gas in 2014? How accurate is this equation based on today's price of gasoline?

 

d) Show how to predict the price of gasoline in 2020 using this equation. Do you think this equation is useful for making accurate predictions? Why or why not?

Answer 1

(a)

The Price function of the gas is P(y) = 0.008y² + 4.830y + 25.720 where y is the year after 1979.

Now the Price of the gas in the year 1980 is

y = 1980 - 1979 = 1

P(1980) = 0.008(1)² + 4.830*1 + 25.720

P(1980) = 0.008 +4.830 + 25.720

P(1980) = 30.558 cents per litre

Therefore Price of the gas in the year 1980 is 30.558 cents per litre.

Answer 2

(b)

The Price function of the gas is P(y) = 0.008y² + 4.830y + 25.720 where y is the year after 1979.

Now the Price of the gas in the year 2000 is

y = 2000 - 1979 = 21

P(2000) = 0.008(21)² + 4.830*21 + 25.720

P(2000) = 3.528 + 101.43 + 25.720

P(2000) = 130.678 cents per litre

Therefore Price of the gas in the year 2000 is 130.678 cents per litre.

Answer 3

(c)

The Price function of the gas is P(y) = 0.008y² + 4.830y + 25.720 where y is the year after 1979.

Now the Price of the gas in the year 2014 is

y = 2014 - 1979 = 35

P(2014) = 0.008(35)² + 4.830*35 + 25.720

P(2014) = 9.8 + 169.05 + 25.720

P(2014) = 204.57 cents per litre

Therefore Price of the gas in the year 2014 is 204.57 cents per litre.

Comparing today's price of Gasoline in canada is on an average of 130 cents per litre.

The Equation is not accurate as it differs by 74 cents per litre or above.

Answer 4

(d)

The Price function of the gas is P(y) = 0.008y² + 4.830y + 25.720 where y is the year after 1979.

Now the Price of the gas in the year 2020 is

y = 2020 - 1979 = 41

P(2020) = 0.008(41)² + 4.830*41 + 25.720

P(2020) = 13.448 + 198.03 + 25.720

P(2020) = 237.198 cents per litre

Therefore Price of the gas in the year 2014 is 237.198 cents per litre.

The price of gasoline in the year 2014 is 204.57 according to the Equation and according to price list its 130 cents per litre.

which means the Equation is not accurate as it differs by 74 cents per litre or above.

If we predict the price of the gasoline by 2020 uing the equation, the price would increase by greater amount.

Therefore we donot prefer using the equation to predict the price of gasoline using this equation.