Thread: Help needed with function in report

Hey Everyone,

I'm writing this report on the ratio between Plugin Electric Vehicles (PEV) and Hybrid Electric Vehicles (HEV) over the next few years, based on given and forecasted values.

These are the values I have (real forecasts by Pike Research):

Year	Total	PEV's	%	HEV's	%
2011	3,222,800	80,745	2.5	3,149,055	97.5
2017	9,730,000	3,639,020	37.4	6,090,980	62.6

For my report I need the percentages of 2012-2016 to create a nice sloped graph and do further calculations. Although I am working with excel, this is a calculus (pre??) problem and the answer is staring in my face, I just don't see it.

function used is: y = c * LN(x) + b
for PEV's:

y = 0,1794 * ln(x) + 0,025

for HEV's:
y = -0,179 * ln(x) + 0,975

So, how do I calculate the percentages for the missing years??? See the attached graph...


Thanks in advance!!!
Rene

Hello Rene,

I'm not sure if you are wanting the percentages projected by the linear or logarithmic regression. If you wanted the logarithmic projections (which I believe would be most useful) all you would have to do is evaluate your known equations at each year, noting that year 1=2011, year 2=2012, and so on.

For example:
y=0.179ln(2)+0.025= 0.149 = 14.9% PEV for year 2.

Arghhhh, is it that simple?? Pls understand, I really suck at any kind of algebraic math, too abstract for me. I'm 50 and unless I finally start to see the light, I'll probably keep running in the dark.

Your answer helps a lot as I have many more of that kind of tables, and yes, I wanted the projections. This was only for Personal Vehicles, it has to be done for Commercial and Motorized 2/3/4 Vehicles too (which obviously have their own totals). Next I have to figure out the CO2 footprints and their CO2 emission so I can make a proper forecast for the next few years.

What I don't understand, however, is where the 0.179 (and -0,1794, though HEV is a downward slope, hense the minus) come from.

Could you please explain that to me? (I substituted the x with a year which gave me rather useless percentages and would never have come up with substituting x with 1,2,... etc)
Cheers

If we know the equation that represents the percentage as a function of time is logarithmic (ie: y=cln(x)+b), then we can start setting up the our equations with the given conditions.

We can use the fact that ln(1)=0 to solve each equation for b.
For PEVs: y=cln(x)+b ---> 0.025=cln(1)+b ---> 0.025=0+b
For HEVs: y=cln(x)+b ---> 0.975+cln(1)+b ---> 0.975=0+b

So we now have b=0.025 for the PEVs and b=0.975 for the HEVs. The next part is a little trickier with the algebra.

Using our data that in 2017 (the 7th year) the percentage for PEVs was 37.4%, we can say:
0.374=cln(7)+0.025 ---> 0.349=cln(7) ---> 0.349/ln(7)=c ---> c = 0.179

Similarly, we can use the conditions for 2017 to solve for c for the HEVs.
0.626=cln(7)+0.975 ---> -0.349=cln(7) ---> -0.349/ln(7)=c ---> c = -0.179

So we can now build our equations for the PEVs and the HEVs
For PEVs: y=0.179ln(x)+0.025
For HEVs: y=-0.179ln(x)+0.975

If you have anymore questions please let me know!

Hey thanks Moebius,

This is an extensive and very clear solution which really does help me a lot, I do see some light twinkle in the dark after all! Good thing too, as I will have to do the same exercise for fossil fuel and natural gas AND all again for commercial vehicles and motorized 2/3/4 wheelers. And as I have developed some innovation which will drastically reduce fuel consumption, I need to do this twice to show before/after innovation graphs. A lotta fun, but a lotta work too!!

Cheers and thanks again!

BTW: can I add u as a friend here? For future reference (no PM ' ing...)

Absolutely! Good luck with everything! I hope it all goes well!

Tnx, and for the heads up: here's the final test result. As you can see the curves and lines perfectly match...

Neat!