EXAMPLE #36 The percent of all families that were
parent families after 1960 was found to be modeled by
y = 1.053x0.888, with x = 0 in 1950.
a. What is f(45)? What does this mean?
b. Does this model indicate that the percent of single
families increased or
decreased during this period after
Root Functionnax a function of the form y = ax1/n or y =
where n is an
integer, n ≥ 2.
The graphs of these functions increase in the first quadrant but not as fast as
y = x does for values of x greater that 1, so we say that they are concave
in the first quadrant.
Graph y = +on [-8,8] by[-8,8]
Graph on [-8,8] by[-8,8] (asymptote)
EXAMPLE #52 The monthly average cost of producing
television sets is dollars, where x
number of sets produced per month. What is the
average cost per set if 2000 sets
EXAMPLE #42 The federal on-budget funds for all
educational programs (in millions of constant 2000 dollars)
between 1965 and
2000 can be modeled by the function
where t is
number of years after 1960.
a. Graph the function for 5 ≤ t ≤ 40. Describe how
the funding for educational
programs varied between
1965 and 2000.
b. What was the amount of funding for educational
programs in 1980?
c. How much federal funding was allotted for
educational programs in 1998?
a. Create a quadratic function that models the data. We
will do this just like alinear regression but we will use
a. Enter the data into List 1 and list 2
b. Then use Stat-cal #5
c. Paste the function
b. Graph the aligned data and the quadratic function on the
same axes. Does this model seem like a reasonable fit?
Example: #4 The following table has the inputs, x, and the
outputs for three functions, f, g, and h. Use the second
difference to determine
which function is exactly quadratic,
approximately quadratic or not quadratic.
Example #18The percent of unemployment in the US for
years 2000-2007 is given by the data in the table below.
a. Create a scatter plot for the data , with x equal to the
number of years after
b. Does it appear that a quadratic model will fit the data? If
so, find the
best-fitting quadratic model.
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