Question

Personal Consumption Although there was an economic
downturn in 2008, personal consumption has
grown overall. Table 11.15 lists (approximate) personal
consumption C in dollars for selected years x.

TABLE 11.15 Personal Consumption (dollars)
x 1959 1982 1990 1998 2009
C $300 $2000 $4000 $6000 $10,000
Source: BEA.

(a)Make a scatterplot of these data. Use the window
[1955, 2010, 10] by [0, 12000, 2000].*


(b) Find a quadratic function given by
C(x) = a(x - 1959)^2 + k
(x) = 3.9(x - 1959)2 + 300
that models the data. Graph C and the data.
(Answers may vary.)*

(c) Estimate when personal consumption was $8000.
Compare your answer to the actual value of 2005.
About 2004; 1 year too soon
(d) Use your function C to predict consumption in
2020 to the nearest thousand dollars.

Answer 1

[C(x)=a(x-1959)^2+K]

a=3.21
K=300

(1959,300)(1982,2000)(1990,4000)(1998,6000)(2009,10000)

Answer 2

Can anyone help with this?

Answer 3

x 1959, 1982, 1990, 1998, 2009
C $300, $2000, $4000, $6000, $10000

C(1959)=a(1959-1959)^2+K
300=a(0)^2+K
300=K

C(1982)=a(1982-1959)^2+300
2000=a(31)^2+300
2000=a(529)+300
1700=529a
3.21=a

Answer 4

Personal Consumption Although there was an economic
downturn in 2008, personal consumption has
grown overall. Table 11.15 lists (approximate) personal
consumption C in dollars for selected years x.

TABLE 11.15 Personal Consumption (dollars)
x 1959 1982 1990 1998 2009
C $300 $2000 $4000 $6000 $10,000
Source: BEA.

(a)Make a scatterplot of these data. Use the window
[1955, 2010, 10] by [0, 12000, 2000].*


(b) Find a quadratic function given by
C(x) = a(x - 1959)^2 + k
(x) = 3.9(x - 1959)2 + 300
that models the data. Graph C and the data.
(Answers may vary.)*

(c) Estimate when personal consumption was $8000.
Compare your answer to the actual value of 2005.
About 2004; 1 year too soon
(d) Use your function C to predict consumption in
2020 to the nearest thousand dollars.

Answer 5

@zepdrix can you help?

Answer 6

This is wearing me out.

Answer 7

me too! lol

Answer 8

The crazy thing is that the word document I am coping from doesn't show b, with the (x)=3.9(x-1959)^2+K.

Answer 9

I have know idea where that is coming from.

Answer 10

I solved for K like this
C(x)=a(x-1959)^2+K
300=a(1959-1959)^2+K
300 =a(0)^2+K
300=K

Answer 11

I used K to find a

C(x)=a(x-1959)^2+K
C(1982)=a(1982-1959)^2+K
2000=a(23)^2+300
2000=a(529)+300
2000=529a+300
2000-300=529a+300-300
1700=529a
3.21=a