Understanding Exponential Growth

Understanding Exponential Growth
Environmental Science 1103 Understanding Exponential Growth

Please use the rule of thumb number (70) to determine some of the answers.

1. The world human population now numbers over 7.2 billion people. (http://www.worldometers.info/world-population/) It is growing at a rate of 1.13% per year. If growth continues at this rate, how long will it take for human numbers to double?
Using this information, project human numbers through 5 population doublings on the chart below.
Population growth
Year Population size (billions)
Now 2016 7.2
1st doubling
2nd doubling
3rd doubling
4th doubling
5th doubling

2. The Grandparents, at the birth of their granddaughter, decide to set up a savings account in her name with an initial deposit of $8,000. No other deposits are ever made into the account. Assume the account yields 7% interest per year.
Question: If the account is left alone, how much money will it contain when the “little” granddaughter decides to cash it all in at age 80?
SHOW YOUR WORK!!!!
3. A typical sheet of paper is approximately 0.1 millimeter (mm) thick. Take a sheet of paper & fold it in half. You have now doubled the thickness to 0.2mm. Fold it again, doubling the thickness to 0.4mm. Keep folding. It gets hard to do this more than 5 times, at which point your wad of paper if 3.2 mm thick. Now, using a calculator or another sheet of paper, continue to fold the paper in your mind.
The question is this: How many times must the paper be folded in half for its thickness to exceed the height of the tallest point in Alaska: Denali (Mt. McKinley)?

SHOW YOUR WORK!!!!

(Denali is over 6190 meters above sea level. That’s over 20,310 feet or 6,190,000 mm high!)

4. Assume a small polluted lake has developed a population of thick, smelly, green scum growing on the water surface. Further assume that the scum doubles in size each day. The people who use the lake are disgusted with this scum & begin to plan how to control the pollution to reduce its growth. As the people are developing the plan, the scum is growing exponentially each day until, on the 29th day, it has covered half of the lake surface.
Question: How much time do the people have to change things before the lake becomes totally covered with scum?

5. The following are currently growing at an exponential rate:

-Carbon dioxide emissions -tropical rain forest destruction
-Human energy use -production of synthetic chemicals
-Creation of deserts -trash production
-Our economy -toxic waste production

Think about the things you have learned about exponential growth in the problems above.

a.) Which of the eight items listed will likely be able to continue exponential growth indefinitely?

b.) Summarize the prospects for exponential growth in a finite space.
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