Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
3rd Edition
ISBN: 9780840064189
Author: Frederick R. Adler
Publisher: Cengage Learning
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Exponential Growth Model
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Chapter 2.1, Problem 25E

a

To determine

To calculate: To find the average rate of change between times 0 and 1.0 from the population size.

a

Expert Solution
Check Mark

Answer to Problem 25E

The average rate of change between times 0 and 1 is 5

Explanation of Solution

Given information: h(t)=5.0t2

Calculation:

  Consider the following equation for a population size.h(t)=5.0t2The population at time t = 0 ish(0)=5×02            =0The population at time t = 1 is shown below:h(1)=5×12            =5                     

The population at time t = 0.1 is

  h(0.1)=5×0.12                 =0.05   

The population at time t = 0.01 is as follows:

  h(0.01)=5×0.012                 =0.0005

The population at time t = 0.001 is

  h(0.001)=5×0.0012                    =0.000005

For a given formula, the average rate of change between times t1 and t2 is

  average rate of change =𑨀h𑨀t                                                 =h(t1)−h(t2)t1−t2

The average rate of change between times 0 and 1 is

  average rate of change =h(t1)−h(t2)t1−t2                                                  =h(0)−h(1)0−1                                                   =0−5−1                                                   =5

b

To determine

To calculate: To find the average rate of change between times 0 and 0.1 from the population size.

b

Expert Solution
Check Mark

Answer to Problem 25E

The average rate of Change between times 0 and 0.1 is 0.5

Explanation of Solution

Given information: h(t)=5.0t2

Calculation:

The average rate of Change between times 0 and 0.1 is shown below:

  average rate of change =h(t1)−h(t2)t1−t2                                                  =h(0)−h(0.1)0−0.1                                                   =0−0.05−0.1                                                   =0.5

c

To determine

To calculate: To find the average rate of change between times 0 and 0.01 from the population size.

c

Expert Solution
Check Mark

Answer to Problem 25E

The average rate of change between times 0 and 0.01 is 0.05

Explanation of Solution

Given information: h(t)=5.0t2

Calculation:

The average rate of change between times 0 and 0.01 is

  average rate of change =h(t1)−h(t2)t1−t2                                                  =h(0)−h(0.01)0−0.01                                                   =0−0.0005−0.01                                                   =0.05

d

To determine

To calculate: To find the average rate of change between times 0 and 0.001 from the population size.

d

Expert Solution
Check Mark

Answer to Problem 25E

The average rate of change between times 0 and 0.001 is 0.005

Explanation of Solution

Given information: h(t)=5.0t2

Calculation:

The average rate of change between times 0 and 0.001 is as follows:

  average rate of change =h(t1)−h(t2)t1−t2                                                  =h(0)−h(0.001)0−0.001                                                   =0−0.000005−0.001                                                   =0.005

e

To determine

To calculate: To find the limit using the obtained values

e

Expert Solution
Check Mark

Answer to Problem 25E

Hence the limit is 0

Explanation of Solution

Given information: h(t)=5.0t2

Calculation:

The limit is 0

f

To determine

To calculate: To graph the tangent line using the obtained values

f

Expert Solution
Check Mark

Answer to Problem 25E

Hence the graph is drawn and the equation of the tangent line is

  h^(t)=h(0)+m(t−0)​​​​​​​​​         =0+0×t          =0

Explanation of Solution

Given information: h(t)=5.0t2

Calculation:

Since the limit is 0, then the slope of the tangent is 0 .

The equation of the tangent line is

  h^(t)=h(0)+m(t−0)​​​​​​​​​         =0+0×t          =0

The graph of the tangent line is shown below:

  Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2.1, Problem 25E

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Chapter 2 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

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