About this Study Set
This study set covers Basic Algebra through
15 practice questions.
Challenging algebraic problems derived from biological constants, environmental data, and animal physiology. Every question includes the correct answer so you can learn as you go — pick any format above to get started.
Questions & Answers
Browse all 15 questions from the
Mathematical Ecology and Natural Algebra study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
The metabolic rate M of a mammal can be approximated by M = k*m^(0.75), where m is body mass. If a species' mass quadruples, by what factor does its metabolic rate increase?
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A
2.83
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B
4.00
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C
5.66
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D
8.00
2
The population growth of a specific bacteria colony follows P = P0 * e^(rt). If r = 0.2 and the population triples, approximately how many units of time t have passed? (Use ln(3) ≈ 1.1)
3
In a stable ecosystem, the predator-prey relationship is modeled by y = ax^2 + bx. If a = -0.5 and b = 10, what is the maximum number of predators (y) that can be supported at a prey level x?
4
The concentration of a pollutant in a pond follows C = k/V. If the volume V of the pond is reduced by 60% due to drought, what is the new concentration relative to the original?
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A
1.67C
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B
2.5C
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C
0.4C
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D
0.6C
5
A forest carbon sequestration model uses the formula S = 200 * log10(A), where A is the area in hectares. To increase sequestration (S) by 200 units, by what factor must the area A be multiplied?
6
The wingspan (w) of a bird species is related to its weight (m) by the equation w = 0.5 * m^(1/3). If a bird's weight increases by a factor of 8, its wingspan increases by a factor of:
7
The sound intensity (I) of a blue whale call follows the inverse square law I = k/d^2. If the distance (d) is tripled, the intensity becomes:
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A
1/3 of I
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B
1/6 of I
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C
1/9 of I
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D
1/12 of I
8
In a pollination experiment, the number of successful seeds (S) is given by S = 50x - x^2, where x is the number of visits. What is the optimal number of visits (x) to maximize seeds?
9
The atmospheric pressure P at altitude h (in km) is P = 101.3 * e^(-0.12h). At what altitude is the pressure approximately half of sea level pressure (101.3)? (Use ln(2) ≈ 0.69)
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A
2.75 km
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B
5.75 km
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C
8.75 km
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D
11.75 km
10
A coral reef's daily growth area follows A = 2 * (1.1)^t. At what time t (in days) does the area quadruple from its initial value? (log1.1(4) ≈ 14.5)
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A
7.25
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B
14.5
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C
29.0
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D
58.0
11
If the gestation period G of a mammal is related to its lifespan L by G = 0.1 * L^(0.5), and a species lives 100 years, what is its gestation period in years?
12
The rate of leaf litter decomposition R is given by R = k * T^2, where T is temperature. If the temperature increases from 10°C to 20°C, the decomposition rate increases by a factor of:
13
For a fish school size N, the oxygen consumption is given by O = N * (100 - 0.5N). At what school size N is the total oxygen consumption zero?
14
The light intensity I at depth d (meters) in the ocean is I = I0 * (0.8)^d. If the intensity is 0.64, what is the depth d?
15
A plant's height h after t weeks is h = 2t^2 + 5. If the plant reaches 77 cm, how many weeks have passed?
