The scatterplot to the left depicts the carbon dioxide(CO2) concentration, in parts per million (ppm) above 250 ppm, in Earth's atmosphere between the years 1850 and 2000. Which of the following functions best models y, CO2 concentration above 250 ppm, x years after 1850?
Answers
Answer:
Co2 levels over time
Global atmospheric carbon dioxide concentrations (CO2) in parts per million (ppm) for the past 800,000 years. The peaks and valleys track ice ages (low CO2) and warmer interglacials (higher CO2). During these cycles, CO2 was never higher than 300 ppm. In 2018, it reached 407.4 ppm.
Answer:
y=0.005x2 - 0.296x + 39.430
Step-by-step explanation:
Based on the choices, we need to select the best quadratic model (whose graph is a parabola) for the scatterplot.
Since all four choices are in intercept form,
y
=
a
x
2
+
b
x
+
c
y=ax
2
+bx+cy, equals, a, x, squared, plus, b, x, plus, c, we can determine the best model by examining the coefficient of the
x
2
x
2
x, squared-term,
a
aa, and the constant term,
c
cc:
If
a
>
0
a>0a, is greater than, 0, then the parabola opens upward. Otherwise, the parabola opens downward.
The
y
yy-intercept of the parabola is located at
(
0
,
c
)
(0,c)left parenthesis, 0, comma, c, right parenthesis.
Hint #2
If we sketch a curve that follows the data points, the curve looks like half of a parabola that opens upward and has a positive
y
yy-intercept.
A curve that follows the data points is a parabola that opens upward and has a positive y-intercept.
25
25
50
50
75
75
100
100
125
125
150
150
20
20
40
40
60
60
80
80
100
100
120
120
y
y
x
x
O
O
Years since 1850
Years since 1850
CO
2
concentration above 250 ppm
CO
2
concentration above 250 ppm
Hint #3
This means for
y
=
a
x
2
+
b
x
+
c
y=ax
2
+bx+cy, equals, a, x, squared, plus, b, x, plus, c, the equation that represents the curve should meet the following criteria:
a
>
0
a>0a, is greater than, 0
c
>
0
c>0c, is greater than, 0
Of the choices provided, only choice (D) meets the criteria:
a
=
0.005
a=0.005a, equals, 0, point, 005 and
c
=
39.430
c=39.430c, equals, 39, point, 430.
Hint #4
y
=
0.005
x
2
−
0.296
x
+
39.430
y=0.005x
2
−0.296x+39.430y, equals, 0, point, 005, x, squared, minus, 0, point, 296, x, plus, 39, point, 430 best models
y
yy, the
CO
2
CO
2
start text, C, O, end text, start subscript, 2, end subscript concentration above
250
250250 ppm,
x
xx years after
1850
18501850.