Concept explainers
(a)
The formula for the sum
(a)
Answer to Problem 38E
Explanation of Solution
The above- ground volume (stern and leaves) of a plant represented by the following equation.
The below-ground volume (roots) of a plant represented by the following equation.
Here, the volumes are measured in
Therefore, the total population is as follows:
(b)
The derivative of each component and the units
(b)
Answer to Problem 38E
The units of rate of change are
Explanation of Solution
The above- ground volume (stern and leaves) of a plant represented by the following equation.
The below-ground volume (roots) of a plant represented by the following equation.
The derivative of each type by differentiating equation (1) and equation (2) with respect to t,
The units of rate of change are
(c)
The derivative of the sum
Whether the
(c)
Answer to Problem 38E
Explanation of Solution
Take the derivative of equation (3) with respect to t,
(d)
The description of happenings in words
(d)
Explanation of Solution
From the rate of change of above-ground volume of a plant, it is observed that the volume is always increasing.
From the rate of change of below-ground volume of a plant, it is observed that the volume is always declining.
From the rate of change of total volume of a plant, it is observed that the volume is always increasing.
(e)
To sketch: A graph of each component and total as functions of time.
(e)
Explanation of Solution
The graph of each component along with the total volume is drawn as
&ems;
Want to see more full solutions like this?
Chapter 2 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
- Find the instantaneous rate of change for each function at the given value. s(t)=4t26 at t=2arrow_forwardThe half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.arrow_forwardUse the total differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the differences in the two results to 4decimal places. (2.9320.942)13arrow_forward
- Find the intensities of earthquakes whose magnitudes are aR=6.0andbR=7.9.arrow_forwardThe kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?arrow_forwardYOUR TURN A 25ft ladder is placed against a building. The base of the ladder is slipping away from the building at a rate of 3ftperminute. Find the rate at which the top of the ladder is sliding down the building when the bottom of the ladder is 7ft from the base of the building.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning