Concept explainers
a
To calculate: To find the average rate of change between times 0 and 1.0 from the population size.
a
Answer to Problem 23E
The average rate of change between times 0 and 1 is
Explanation of Solution
Given information:
Calculation:
Consider the equation for a population size.
The population at time
The population at time t = 1 is shown below:
The population at time t=0.1 is
The population at time t=0.01 is as follows:
The population at time t=0.001 is
For a given formula, the average rate of Change between times
average rate of change
The average rate of change between times 0 and 1 is
b
To calculate: To find the average rate of change between times 0 and 0.1 from the population size.
b
Answer to Problem 23E
The average rate of change between times 0 and 0.1 is
Explanation of Solution
Given information:
Calculation:
The average rate of change between times 0 and 0.1 is shown below:
c
To calculate: To find the average rate of change between times 0 and 0.01 from the population size.
c
Answer to Problem 23E
The average rate of change between times 0 and 0.01 is
Explanation of Solution
Given information:
Calculation:
The average rate of change between times 0 and 0.01 is
d
To calculate: To find the average rate of change between times 0 and 0.001 from the population size.
d
Answer to Problem 23E
The average rate of change between times 0 and 0.001 is
Explanation of Solution
Given information:
Calculation:
The average rate of change between times 0 and 0.001 is
e
To calculate: To find the limit using the obtained values
e
Answer to Problem 23E
The limit is 0.405.
Explanation of Solution
Given information:
Calculation:
(e) The limit is 0.405.
f
To calculate: To graph the tangent line using the obtained values
f
Answer to Problem 23E
Hence the graph is drawn and the equation of the tangent line is
Explanation of Solution
Given information:
Calculation:
Since the limit is 0.405, then the slope of the tangent is 0.405.
The equation of the tangent line is
The graph of the tangent line is shown below:
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