# Precalculus Project Hybrid

The patented Hybrid Synergy Drive uses an electric motor and gasoline engine to drive a vehicle. This system combined with a continuous variable transmission (CVT) AND aerodynamic design allows a vehicle to achieve maximum fuel efficiency without sacrificing speed and range.

In this project we will formulate functions for different driving conditions and combine them to predict fuel economy for different trip. Secondly we will look at the average fuel economy of a car and determine functions the costs of running a car based on miles traveled, mpg and cost of gas.

PART 1 LEVEL TERRAIN: On level terrain in a certain hybrid car, the mpg is 45 from combination of the gas engine and electric motor a) Find a formula for gallons of gas used G1 as a function of miles X1 traveled on level terrain. b) Calculate G2(60). Explain the practical meaning of the question and answer you have obtained.

PART 11 DOWNHILL: If the hybrid car is going downhill, the mpg is 100 since it is in all electric mode. a) Find a formula for gallons of gas used G2 as a function of miles X2 traveled downhill. b) Calculate G2(60). Explain the practical meaning of the question and answer you have obtained.

PART 111 UPHILL: When traveling uphill, the hybrid car uses mostly the gasoline engine with the electric motor for added power, but the mpg is variable depending on the grade of the hill, and so uphill the car gets anywhere from 8 to 40 miles per gallon. More specifically on a 6% grade up, the car will consume 18 miles per gallon. In addition, the mpg UPHILL is inversely proportional to the SQUARE ROOT of the grade of the hill (as a percent-don't convert to a decimal). a) Find a formula for uphill fuel economy F (in mpg) as a function of grade of hill (in percent) g. (hint: see variation in text). [In reality, speed also plays an important part, but we'll ignore this to simplify the problem.] b) Find a formula for gallons of gas used G3 as a function of miles traveled uphill X3 and F, fuel economy uphill. Then write G3 in terms of X3 and g- in other words write the formula for G3 of F (G3 composed with F) c) Suppose you drive this hybrid car 15 miles straight up a hill with a 3% grade, how many gallons of gas would you use (in other words calculate G3(15,3%) and explain it's meaning).

PART IV- put it all together Construct an equation for total consumption (in gallons) C as a function of miles of level terrain (X1), downhill terrain (X2) and miles uphill X3 with grade g. In other words find an equation for: C(X1, X2, X3, g) a) Suppose you drive 500 miles with this hybrid car. For 212 miles the terrain is mainly level. For 91 miles the road is all downhill. And for the rest, the road is uphill at a 2% grade. How many gallons of gasoline do you consume? b) What is your average fuel economy for this 500 mile trip? c) BONUS: from the previous question, suppose the uphill grade for 150 miles is at 1% and the grade for the remainder of the uphill portion (47 miles) is 3%. How does this change your answer from part a and b above? Show work.

PART V GAS CONSUMPTION a) Fina an equation for V for the total cost of gas for a vehicle as a function x miles driven per year, an average mpg of m, and an average cost of gas of d dollars per gallon. b) Suppose a new hybrid vehicle gets 50 mpg and your current car gets 22 mpg. Assuming gas is 4.00 per gallon and you drive 12,000 miles per year, how much will you save by switching to a hybrid vehicle. Suppose you had to make a monthly payment of 250 dollars to have the hybrid, is it still worth it? Explain. c) Show different scenarios of yearly mile driven, cost of gas and mpg for your current car to illustrate different savings.

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Tag is functional-equations? –  Euler....IS_ALIVE Sep 19 '12 at 22:05
What have you tried? Where are you stuck? Do you want us to write the whole paper for you? –  Ross Millikan Sep 19 '12 at 22:07
i didn't mean for it to be functional-equations. I have tried some, but honestly i don't know where to start. I was hoping that someone could help me start and work with me to get through it. That way i can learn and know if i'm doing it correctly. –  kourtnee Sep 19 '12 at 22:37
Any kind of help would be greatly appreciated. It is due in the next few days and I have been busting my butt to try and understand it. :( –  kourtnee Sep 19 '12 at 22:48
well but that issue is this? is about functions? –  user41858 Sep 19 '12 at 23:32

You are given a detailed roadmap for a paper to write. What class is it for? It appears you are supposed to convince the reader that a hybrid will save money in the long run. Most of the sentences give you an equation to write and some values to plug into it. For example, Part Ia says $G1 \text{gallons used}= \frac {X1\text{miles}}{45 \text{miles/gallon}}$. For Ib I think you have a typo and it should be compute $G1(60)$. Then "Explain the practical meaning of the question and answer you have obtained." So do so, then go on to Part II.

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The class is precalculus. So you just do a random number of miles divided by 45 mpg? –  kourtnee Sep 20 '12 at 0:46
@kourtnee: that is the 60. I didn't read it all but I would guess you are comparing the fuel use of a hybrid over a trip with a standard car. –  Ross Millikan Sep 20 '12 at 1:29
Okay, i'm sorry that i seem so clueless, but i am. Haha. I have some equations written down, but i'm sure i'll end up getting a bad grade lol. –  kourtnee Sep 20 '12 at 1:38