I need help to see if I did these steps and problems right before I hand this in…I am stuck, and cannot figure out question three part b and H…I just need help with the proper function of b and h part.

1. An anthropologist drives a car at a speed of 30 mph along a straight road in Giza, Egypt while on a discovery trip. The distance traveled by the anthropologist as a function of time t is given as where represents the anthropologist’s initial position.

a) What are the independent & dependent variables in this problem? What does the value 30 mph represent in this function? Explain

The independent variable is the time being traveled by the car, and the dependent variable is the distance traveled.

In this function, D(t)=30t+ the value 30 mph represents the miles per hour the car travels; the distance that the car travels will depend on the time traveled …in this case the car travels 30 miles per hour.

b) The initial position of the anthropologist’s vehicle at the start of time is t = 0. Find if the vehicle’s starting point is 15 miles ( ) from the hotel where he was staying. Explain what your answer means.

So, d of 3 is 105 miles
This means that the distance traveled from the initial starting point which was 15 miles from the anthropologist’s hotel was 105 miles.

c) If you were to graph D (t), what would be an appropriate domain? Range? Explain your reasoning.

If I were to graph this, the appropriate domain, considering that the domain is the set of inputs, and all real numbers, would be the first coordinate of the ordered pair. In question b, I got: d of 3 is 105…(3,0) Therefore, I would graph, or plot 3.

2. A small town, outside of Giza, has been experiencing a boom in population growth. By the end of 2003, the population had grown to 45,000, and by 2008, the population had reached 60,000.

a) Using the formula for slope as a model, find the average rate of change in population growth, expressing your answer in people per year.

Rate of change 45,000-60,000/2033-2008
Rate of change= 3 thousand per year growth.

b) Using the average rate of change determined, predict the population of this town in the year 2012. What about 2020?

From 2008 to 2012, there is a 4 year difference. Considering there is a 3,000 a year population growth or rate of change the population will be 72,000. In 2020 the population will be 96,000.

c) Write an equation of the line that represents this population growth.

d) What is the y-intercept? What does the y-intercept represent? What does it represent as it pertains to this problem?

The y intercept is 3,000. The y intercept represents the rise, or change in y, which in this case represents the average population growth per year.

When the remains of ancient people are discovered, anthropologists can use the bones that are found to determine a person’s height. Using the length of the tibia bone and the linear equations H = 0.944T + 28.6 for males and H = 0.984T+ 28.6 for females, they can determine the heights of the ancient people. (H represents the height in inches and T represents the length of the tibia bone in inches.)

a) What would be the height of a man whose tibia bone measures 43.4 inches? Show how you arrived at your answer.

If H represents height, and T represents length of the tibia, using the linear equation for a male I would start out by writing the equation H=0.944t+28.6 like this:

H (t) =0.944(43.4) +28.6

H (t) =40.9696+28.6

H (t) =69.5696 inches
If I convert to feet he was 5 foot and 9.56 inches

b) A woman measures 5ft 5in, what would be the length of her tibia bone? Show how you arrived at your answer.

5 foot, 5 inches = 66 inches, so, I would write the problem like this

c) What is the slope, or rate of change, for the equation representing the height of the man?

The slope or rate of change is 0.944

d) What is the slope, or rate of change, for the equation representing the height of the woman?

The slope or rate of change for the equation representing the woman is 0.984

e) What is the y-intercept of the given equations? Given the real-world situation represented here, would the y-intercept be a value that would make sense? Justify your answer.

The y-intercept is (0, 28.6). If this was a real world situation than yes, it is a constant and corresponds to a natural length.

f) Given that T represents the values in the domain of the functions above, are there any values of T that would be inappropriate for this situation?

Yes, zero and negative values

g) If you were to graph these two equations would you expect the lines to be intersecting, parallel or perpendicular?
Justify your answer.

Separately, it would be a horizontal line. Because x is missing, t any number can substitute, thus the ordered pairs would be solutions. But If I graphed each one the lines would be horizontal parallel to the x-axis.

h) On September 17, 2009, Turk Sultan Kosen was declared to be the world’s tallest man at a height of 8ft 1in tall. What would be the length of his tibia bone? Show how you arrived at your answer.

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