Culminating task

ou are going to make a pitch to the hosts of a reality TV show where entrepreneurs request funding for projects or products that are designed to improve communities.

Your pitch must combine a compelling reason why your initiative should be supported, with evidence that justifies the need for action. You will research and collect secondary data, use the data to create graphical and algebraic models, make predictions based on your algebraic model, and create a visual presentation using the media/platform of your choice. Some example options are PowerPoint, WordPress, Prezi, Weebly, iMovie, Show Me, Blogger, Tumblr, YouTube, etc.

The function used to create your algebraic model must be one of the types of functions covered in this course (polynomial of degree 3 or higher, exponential, logarithmic, or trigonometric).

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Identify and describe a community issue and a proposed way to reduce impact and/or improve outcomes. As an example, the proposal could be a campaign to convince people to change daily habits that are harmful to the community. Or you may propose the development of a new product or process that can help to address a community issue. The proposal could also be an initiative that creates awareness of a local, national, or global issue.

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Research secondary data from a reliable source and create a mathematical model to predict outcomes if no action to reduce harmful effects is taken.

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Create algebraic and graphic representations of your model and provide a brief, but convincing, description of the benefits of your proposal

MHF4U Learning Activity 4.9

Sample Culminating Task

TVO ILC

MHF4U

Sample Culminating Task
Hello Dragons, thank you for taking the time to read my proposal today.

I’m here to talk about BHamBew®, a new product taking the world by storm to reduce the
damage to the environment caused by deforestation.

The issue

The facts are simple: Since 1990, the world is using up its forests faster than it is replacing
them. While sustainability initiatives in some countries are helping, there’s still a loss of trees
that is threatening ecosystems, air quality, and employment security around the world.

The product

BHamBew®, Bamboo Hamperers Beware, is investing in bamboo plants to replace the wood
fiber used in many products. Bamboo is easier to grow, faster to replenish, and produces
higher-quality products. I’m asking you to invest in BHamBew® to help us expand our operation
to two new countries to protect forests and create jobs there.

The data

Since 1990, the percent of land in low-income countries that is covered in forest has gone down
by almost 3%. In high-income countries, the forest percentage has gone up in that same time.
Clearly, we need to do something to reverse the trend in low-income countries.

Forest area (% of land area)

Year High income Low Income

1990 28.44592039 32.94659862

1991 28.47271714 32.85224391

1992 28.49973554 32.7554647

1993 28.52614108 32.0496949

1994 28.55245764 31.95841427

1995 28.57883115 31.86319081

1996 28.60518873 31.76773419

1997 28.5758657 31.65825893

1998 28.60219675 31.56507314

1999 28.62852019 31.46895801

2000 28.64767011 31.3734004

2001 28.65863294 31.29142374

2002 28.66882846 31.20943362

2003 28.67916468 31.1272775

2004 28.69006026 31.04612382

Forest area (% of land area)

Year High income Low Income

2005 28.70092618 30.96406075

2006 28.71284367 30.88142178

2007 28.72424655 30.79839095

2008 28.74783578 30.71859638

2009 28.75841672 30.63560245

2010 28.76858587 30.55160083

2011 28.80271107 30.48272078

2012 28.83933036 30.41486873

2013 28.87221907 30.34621735

2014 28.90624946 30.27772834

2015 28.94071418 30.20922847

2016 28.96640652 30.13852152

MHF4U Learning Activity 4.9

Sample Culminating Task

TVO ILC

The reference

World Bank, Environment Indicators. (2020). Forest area (% of land area) [Data File]. Retrieved
from https://data.worldbank.org/indicator/AG.LND.FRST.ZS

The plot

The model

Using polynomial regression, I determined that an appropriate model for the Forest Area of low
income countries is y = -0.0002×3 + 0.0117×2 – 0.957x + 33.234; R² = 0.8875 where x is the
number of years since 1990

The explanation

I noticed that the current view of the data showed a decline that is slowing down slightly. I
thought about using a negative logarithm (a vertical reflection and translation up), but I do not
believe that the pattern will slow down logarithmically without external factors. I could have also
used exponential decay, but felt that there shouldn’t be a horizontal asymptote (unless it’s at
zero, which would not match this pattern). That left me with polynomials. I recognized that the
smallest degree polynomial is best, as higher degree polynomials can always approximately
match data without extrapolating well. Using a degree three (cubic) polynomial, I applied
Microsoft Excel to find the pattern.

https://data.worldbank.org/indicator/AG.LND.FRST.ZS?end=2016&start=1990&view=chart

MHF4U Learning Activity 4.9

Sample Culminating Task

TVO ILC

The domain

My function should be able to represent data in the past. I plotted my graph on GeoGebra, and
found that it crossed y = 100 at x = -50. This means that using my model, the low-income
countries would have been 100% covered in forest in 1940. That doesn’t sound possible
(because people live there and build houses), so I feel that an appropriate domain for my model
starts around x = -30, or 1960. Continuing forward with the pattern, I notice that after x = 72, the
forest area would be lower than zero. This isn’t possible either, so I think my model’s domain
should end at x = 70, or 2060.

The graph of the model

If we continue to do nothing, my mathematical models predict that we will run out of forests in
low income countries by 2060 (70 years after the data begin in 1990).

As you can see from the algebraic model y = -0.0002×3 + 0.0117×2 – 0.2757x + 33.234; R² =
0.9875, the rate of deforestation is currently slowing down. We can’t let that relax us! According
to this model, the pattern is just slowing down temporarily. It will soon begin to decrease even
faster.

MHF4U Learning Activity 4.9

Sample Culminating Task

TVO ILC

The calculation

Noticing that low income forest areas are going down while high income areas are going up, I
want to know when they’ll meet. The model for low income areas is y = -0.0002×3 + 0.0117×2 –
0.2757x + 33.234. I can create a model for high income areas as well. It gives me y = 0.0002×2
+ 0.0115x + 28.474. Those two graphs will meet when 0.0002×2 + 0.0115x + 28.474 = -0.0002×3

+ 0.0117×2 – 0.2757x + 33.234.

0.0002𝑥2 + 0.0115𝑥 + 28.474 = −0.0002𝑥3 + 0.0117𝑥2 − 0.2757𝑥 + 33.234

0.0002𝑥3 − 0.0115𝑥2 + 0.2872𝑥 − 4.76 = 0

2𝑥3 − 115𝑥2 + 2872𝑥 − 47600 = 0
(𝑥 + 10.9)(𝑥 − 34.2)2 = 0

𝑥 = −10.9 𝑜𝑟 𝑥 = 34.2

This tells me that the values were about the same 11 years before 1990 (in 1979, which is in the
domain) and will be again 34 years after 1990, in 2024 (which is also inside the domain).

The sales pitch

Notice that the forest area in low income countries is going down. That’s because wood fiber is
much cheaper in those countries than in high income countries. It’s also less expensive to pay
for labour. Join me, Dragons, in investing in BHamBew® in these low income countries. We can
use some of the deforested areas to plant bamboo and use that for future textile sales. Bamboo
grows quickly, and the labour that’s currently working in logging operations can help us out. We
can even reuse their infrastructure. Since we can grow more bamboo than trees, we don’t need
as much land – we will even use some of the proceeds to replant trees. Our product will be
reliable, efficient, and help the environment. What an opportunity!

Thanks for your time, Dragons. You can write me a cheque or send an e-transfer.

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