Derivative and Heart Beats
MAT 115.1647
Gerard Martinez
Md Habib
APPLICATIONS OF FUNCTIONS PROJECT
1. Exercise and heart rate: The data in the table below represent the maximum benefit to the heart from exercising, if the heart rate is in the target heart rate zone.
Age, x
Maximum number of heart beats, y
20
140
30
133
40
126
50
119
60
112
70
105
a) Plot the data in the table above. What kind of pattern can you observe from your graph?
b) What type of relationship appears to exist between the maximum number of heart beats and age? The maximum number of heart beats decreases as the age increases.
c) Select any two points to find the average rate of change, and the function, determine whether the function is linear or not.
(70,105),(60,112) =
x + 14 Yes, the function above is linear.
d) Using the above function to predict the maximum number of heart beats for ages of 25, 55, 65 and 80. heart beats
At the age of 25 the max # of heart beats is 136.5.
heart beats
At the age of 55 the max # of heart beats is 115.5.
(65) + 154 heart beats
At the age of 65 the max # of heart beats is 108.5.
heart beats
At the age of 80 the max # of heart beats is 98.
e) Using the above function what is the approximate age of a person whose maximum number of heart beats is 115?
f) Does the relationship defined by the set of ordered pairs (x, y) represent a function? If yes, write the domain and range.
- Yes, the ordered pairs represent a function the range is , and the domain is
2. Healing of Wounds. The normal healing of a wound can be modeled by an exponential function.
If A0 represents the original area of the wound and if A equals the area of the wound after n days, the function
A(n) = A0 e - 0.35n describes the area of the wound on the nth day following the injury when no infection is present to retard the healing. Suppose that the wound initially had an area of 100 square
Gerard Martinez
Md Habib
APPLICATIONS OF FUNCTIONS PROJECT
1. Exercise and heart rate: The data in the table below represent the maximum benefit to the heart from exercising, if the heart rate is in the target heart rate zone.
Age, x
Maximum number of heart beats, y
20
140
30
133
40
126
50
119
60
112
70
105
a) Plot the data in the table above. What kind of pattern can you observe from your graph?
b) What type of relationship appears to exist between the maximum number of heart beats and age? The maximum number of heart beats decreases as the age increases.
c) Select any two points to find the average rate of change, and the function, determine whether the function is linear or not.
(70,105),(60,112) =
x + 14 Yes, the function above is linear.
d) Using the above function to predict the maximum number of heart beats for ages of 25, 55, 65 and 80. heart beats
At the age of 25 the max # of heart beats is 136.5.
heart beats
At the age of 55 the max # of heart beats is 115.5.
(65) + 154 heart beats
At the age of 65 the max # of heart beats is 108.5.
heart beats
At the age of 80 the max # of heart beats is 98.
e) Using the above function what is the approximate age of a person whose maximum number of heart beats is 115?
f) Does the relationship defined by the set of ordered pairs (x, y) represent a function? If yes, write the domain and range.
- Yes, the ordered pairs represent a function the range is , and the domain is
2. Healing of Wounds. The normal healing of a wound can be modeled by an exponential function.
If A0 represents the original area of the wound and if A equals the area of the wound after n days, the function
A(n) = A0 e - 0.35n describes the area of the wound on the nth day following the injury when no infection is present to retard the healing. Suppose that the wound initially had an area of 100 square