Since 1990, the number of new books published each year has been growing at a rate that can be
approximated by a quadratic function. The table
shows the number of books published in the
United States for selected years. Use the
regression feature on your calculator to
determine the quadratic which best fits the
data. Then, estimate the number of books in
2017. (Hint: 2017 represents when x = 27)
Years (1990=0) Books Published (1000's)
46.7
49.2
3
49.8
4
51.7
5
62.0
6
68.2
7
65.8
9
102.0
10
122.1
0
2
Oy=1.0622 - 3.57x + 49.8726150
o y = 1.0522 - 3.682 + 49.9 715990
Oy=1.04.c– 3.51x + 49.41 712800
y = 1.0522 - 3.752 + 49.6 713800

Option (3)

Step-by-step explanation:

By using quadratic regression calculator,

Regression equation for the given data will be,

y = -1.04x²- 3.51x + 49.41

For x = 27 years (In year 2017),

y = 1.04(27)² - 3.51(27) + 49.41

  = 758.16 - 94.77 + 49.41

  = 712.8

Since y-values are in thousand (000's)

Therefore, number of books published in 2017 will be 712800.

Option (3) will be the correct option.

i would need to see the dot plot : )

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for