a.
To find:The mass density of the material of an insect as a function of time.
a.
Answer to Problem 36E
The density of the material of insect as the function of time is
Explanation of Solution
Given: The given mass function
Concept Used:
The mass M of an object is related to volume V of the object according to relation
Calculation:
The mass and volume of the insect are functions time given as
Therefore, the density of the material the insect is made of is also time dependent given by
Conclusion:
The density of the material of insect as the function of time is
b.
To find:The derivative of the density
b.
Answer to Problem 36E
The derivative of density
Explanation of Solution
Given:
The expression for density is
Formula used:
The derivative of function
Calculation:
The density isthe function of t given by
Now, the derivative of
Conclusion:
The derivative of density
c.
To find: At what time the density
c.
Answer to Problem 36E
The density will increase when
Explanation of Solution
Given:
The derivative density computed in part (a) as a function of time is
Concept used:
A function
Calculation:
The derivative of density is
The density will increase when
Conclusion:
The density will increase when
d.
To graph:The density given in part (a) for first 5 days.
d.
Explanation of Solution
Given:
The density function computed in part (a)
Concept used:
We use graphing calculator for the graph.
Graph:
The graph of the function
Interpretation:
We see clearly that the function
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Chapter 2 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
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