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(10551)  (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: 
|
|
|
