SOLUTION: The table lists a readings for three years. ​(a) If the quadratic relationship between the carbon dioxide concentration C and the year t is expressed as Upper C equals at squar

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Question 1154243: The table lists a readings for three years.
​(a) If the quadratic relationship between the carbon dioxide concentration C and the year t is expressed as Upper C equals at squared plus bt plus c​, where t equals 0 corresponds to​ 1962, use a system of linear equations to determine the constants​ a, b, and​ c, and give the equation.
​(b) Predict the year when the amount of carbon dioxide in the atmosphere will double from its 1962 level.
Year
1962
1992
2022
CO2
318
341
371
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
---------
expressed as Upper C equals at squared plus bt plus c​,
---------




-----------
Year
1962
1992
2022
CO2
318
341
371
----------- 
Year     t            Levels
1962      0               318
1992     30               341
2022     60               371       - this has not happened yet.

Variable t was an adjustment from the given year data for easier computation for the steps and the model.

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

The table lists a readings for three years.
(a) If the quadratic relationship between the carbon dioxide concentration and the year is expressed as , where equals corresponds to , use a system of linear equations to determine the constants, , and , and give the equation.
table:
|
|
|
|



since equals corresponds to , and is



................year , , ,


.......solve for

.................eq.1

................year , , ,




........eq.2

from eq.1 and eq.2 we have





go to
.................eq.1, plug in


your equation is:



(b) Predict the year when the amount of carbon dioxide in the atmosphere will double from its level.
level is
in years will double which is
.........sole for



using quadratic formula, we get

=> we need only positive root, we will disregard negative solution

-> exact solution
-> approximately

years from is: the year and the amount of carbon dioxide in the atmosphere will double from its level.




Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The table lists a readings for three years.
​(a) If the quadratic relationship between the carbon dioxide concentration C and the year t is expressed as Upper C equals at squared plus bt plus c​, where t equals 0 corresponds to​ 1962, use a system of linear equations to determine the constants​ a, b, and​ c, and give the equation.
​(b) Predict the year when the amount of carbon dioxide in the atmosphere will double from its 1962 level.
Year
1962
1992
2022
CO2
318
341
371
The equation that person gave you is WRONG!! You need to get the correct one!! 

Anyway, when you do, the amount of time that it'll take for the carbon dioxide concentration to double from its 1962 level, 

or from 318 to 636 is:  

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