Differential equations 9. Write the differential equation that describes the following relationships. [6 pts total] a. The rate of growth in biomass of a tree, B'(t), is equal to the square root of its biomass, B(t) b. The rate at which carbon accumulates in the atmosphere C'(t) is equal to the rate of human carbon emissions, E(t), minus the amount of carbon in the atmosphere C(t) times an ocean uptake multiplier (parameter), h, minus the amount of carbon in the atmosphere C(t) times the amount of terrestrial living biomass B (t) times a terrestrial growth multiplier (parameter), n. C. The rate at which water changes in a reservoir (like Lake Cachuma), W'(t), is equal to the runoff in the watershed, R(t), plus the direct precipitation on the reservoir P(t), minus a percentage (parameter), h, of the amount of water in the reservoir itself, W (t), which is drawn for human use.
Differential equations 9. Write the differential equation that describes the following relationships. [6 pts total] a. The rate of growth in biomass of a tree, B'(t), is equal to the square root of its biomass, B(t) b. The rate at which carbon accumulates in the atmosphere C'(t) is equal to the rate of human carbon emissions, E(t), minus the amount of carbon in the atmosphere C(t) times an ocean uptake multiplier (parameter), h, minus the amount of carbon in the atmosphere C(t) times the amount of terrestrial living biomass B (t) times a terrestrial growth multiplier (parameter), n. C. The rate at which water changes in a reservoir (like Lake Cachuma), W'(t), is equal to the runoff in the watershed, R(t), plus the direct precipitation on the reservoir P(t), minus a percentage (parameter), h, of the amount of water in the reservoir itself, W (t), which is drawn for human use.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![Differential equations
9. Write the differential equation that describes the following relationships. [6 pts total]
a. The rate of growth in biomass of a tree, B'(t), is equal to the square root of its biomass, B(t)
b. The rate at which carbon accumulates in the atmosphere C'(t) is equal to the rate of human carbon
emissions, E(t), minus the amount of carbon in the atmosphere C(t) times an ocean uptake multiplier
(parameter), h, minus the amount of carbon in the atmosphere C(t) times the amount of terrestrial
living biomass B (t) times a terrestrial growth multiplier (parameter), n.
C.
The rate at which water changes in a reservoir (like Lake Cachuma), W'(t), is equal to the runoff in the
watershed, R(t), plus the direct precipitation on the reservoir P(t), minus a percentage (parameter), h,
of the amount of water in the reservoir itself, W (t), which is drawn for human use.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c27c061-d16a-4075-8bdf-3e6d2b43249c%2F70b13cef-af61-468b-951f-52212538fc4f%2Fpalw9uq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Differential equations
9. Write the differential equation that describes the following relationships. [6 pts total]
a. The rate of growth in biomass of a tree, B'(t), is equal to the square root of its biomass, B(t)
b. The rate at which carbon accumulates in the atmosphere C'(t) is equal to the rate of human carbon
emissions, E(t), minus the amount of carbon in the atmosphere C(t) times an ocean uptake multiplier
(parameter), h, minus the amount of carbon in the atmosphere C(t) times the amount of terrestrial
living biomass B (t) times a terrestrial growth multiplier (parameter), n.
C.
The rate at which water changes in a reservoir (like Lake Cachuma), W'(t), is equal to the runoff in the
watershed, R(t), plus the direct precipitation on the reservoir P(t), minus a percentage (parameter), h,
of the amount of water in the reservoir itself, W (t), which is drawn for human use.
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