Suppose that the organisms learn to colonize other planets and moons in their solar system. The total surface area of the worlds in their solar system that could potentially be colonized is roughly five times the surface area of their current home planet. Under the assumptions of part (c), could the organisms fit in their solar system in the year 2200? Explain.
Suppose that the organisms learn to colonize other planets and moons in their solar system. The total surface area of the worlds in their solar system that could potentially be colonized is roughly five times the surface area of their current home planet. Under the assumptions of part (c), could the organisms fit in their solar system in the year 2200? Explain.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that the organisms learn to colonize other planets and moons in their solar system. The total surface area of the worlds in their solar system that could potentially be colonized is roughly five times the surface area of their current home planet. Under the assumptions of part (c), could the organisms fit in their solar system in the year 2200? Explain.
Transcribed Image Text:An organism's population in the year 2000 was about 8 billion and was increasing with a double time of 10 years. Suppose the population continued this growth pattern from the year 2000 into the future. Complete parts (a) through (d) below.
a. Extend the following table, showing the population at 10-year intervals under this scenario, until reaching the year 2200.
Year
Population Year
2070
8×10⁹
1.6×1010 2080
3.2×1010 2090
6.4×1010 2100
1.28×1011
2110
2.56×1011
2120
2060
5.12×1011 2130
2200
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
2000
2010
2020
2030
2040
2050
12
Population
1.024 × 10
2.048 × 1012
4.096 × 1012
8.192×1012
13
1.6384 × 10
13
3.2768 × 10
6.5536 × 10
2030
13
Year
2140
2150
2160
2170
2180
2190
Population
1.31072 × 1014
2.62144×1014
5.24288 × 1014
1.048576x10¹
15
15
2.097152 × 10
15
4.194304 x 10
8.388608 x 10
15
b. The total surface area of the planet the organisms inhabit is about 5.1 × 10¹4 m². Assuming that the organisms could occupy all this area, to the nearest 10 years, approximately when would the organisms be so crowded that every
organism would have only 1 m² of space?
Between 2150 and 2160
(Use ascending order.)
c. Suppose that, when the area needed to grow food and find other resources is taken into account, each organism actually requires about 104 m² of area to survive. To the nearest 10 years, about when would this limit be reached?
d. Suppose that the organisms learn to colonize other planets and moons in their solar system. The total surface area of the worlds in their solar system that could potentially be colonized is roughly five times the surface area of their current
home planet. Under the assumptions of part (c), could the organisms fit in their solar system in the year 2200? Explain.
The organisms could not fit because they would need about 6.19838951 × 1020 m² of area to survive and there would be 25.5×10¹4 m² available.
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
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