y=59.617+1.18t/1+0.012t

Question

A model that represents the data is given by:

y=59.617+1.18t/1+0.012t

 

0 less than equal to t less than or equal to 70

 

where t is the time in years, with t =0 corresponding to 1930.

 

a) use graphing utility to graph the data from the table above and the model in the same viewing window. How well does the model in the fit the data? Explain

 

b) find the y-intercept of the graph of the model. What does it represent in the context of the problem?

 

c)use the zoom and trace features of the graphing utility to determine the year when the life expectancy was 73.2. Verify your answer algebraically.

 

d) determine the life expectancy in 1948 both graphically and algebraically.

 

e) use the model to estimate the life expectancy of a child born in 2020.

Answer 1

I assume the function is

 

y = (59.617 + 1.18t) / (1 + 0.012t)

 

 

a)

 

Use a graphing calculator to graph this function.  Press the Y= button.  This will allow you to enter your function exactly as you have it.  Type in the function.  Next, press the WINDOW button.  This will allow you to change your graph size and scale.  Set these parameters:

 

Xmin = 0

Xmax = 70

 

 

Finally, press GRAPH to see the calculator construct your graph.

 

You can also see your table by pressing 2ND and then GRAPH.

 

 

b)

 

To find the y-intercept, evaluate the function when t=0.  The y-intercept represents the life expectancy at the year 1930.

 

 

c)

 

Press the TRACE button on your graphing calculator.  You will see a cursor at some point on the graph.  Move that cursor by pressing the arrow keys on your calculator until you see y=73.2.   What is the x value when y=73.2?   Add that x value to 1930 since t=0 represents the year 1930, to obtain your actual year.

 

 

d)

 

Algebraically:  evaluate y when t=18.

 

Graphically:  Press 2nd and CALC on the calculator.  Then you press value.  It will allow you to type in an x value.  You will see your cursor next to x=.   Press the number 18, hit Enter, and see the y value appear.  This y value must the same as your algebraic answer.

 

 

e)

 

Evaluate y when x=90.