Question

In addition to the changes within each year, what changes in CO2 concentration occurred between 1990 and 2010? Calculate the average CO2 concentration for the 12 months of each year. By what percentage did this average change from 1990 to 2000 and from 1990 to 2010?

Short answer

CO₂ concentration was increased in 2010 in comparison to 1990. The average CO₂ concentration for the 12 months of each year will be derived by dividing the total concentrations of CO₂ by 12.

Here, the average for 1990 will be 354.51, for 2000 it will be 369.40, and for 2010 it will be 389.77. The average changed from 1990 to 2000 by 4.2 percent, and from 2000 to 2010 it will be 5.51 percent.

Step-by-step solution

Step 1: Average

An average is a single number representing a large set of numbers. It represents all numbers available in the data. It is calculated by dividing the total values of data by the number of data.The average value represents quantities that change their values. Thus it is helpful in quickly summarizing the data.

Step 2: Percent change

Percent change is a mathematical concept that explains the degree of change during the time duration. It can be calculated by the formula:

\[percent{\rm{ }}change = \frac{{(Final\,value - Initial\,value)*100}}{{Initial\,value}}\]

Step 3: Calculations about CO2 concentrations

According to the given data, in all the months, CO₂ concentrations were more in 2010 than in 1990. After adding all the concentrations of CO₂ in 1990, the average will be:

\[average = \frac{{Total{\rm{ }}of{\rm{ }}all\,concentration}}{{number{\rm{ }}of\;months}}\]

\(average(1990) = \frac{{4,254}}{{12}}\)

\(average = 354.51\)

\(average\;(2000) = \frac{{4,433.23}}{{12}}\)

\(average\;(2000) = 369.40\)

\(average\;(2000) = \frac{{4,677.35}}{{12}}\)

\(average\;(2000) = 389.77\)

Percentage change of CO2 concentration in 1990 to 2000-

\[percent\;change = \frac{{(Final\;value - Initial\;value)*100}}{{Initial\;value}}\]

\[percent{\rm{ }}change = \frac{{(369.40 - 354.51)*100}}{{354.51}}\]

\(Percent\,change = 4.2\% \)

Percentage change of CO2 concentration in 2000 to 2010-

\[percent\;change = \frac{{(389.77 - 369.40)*100}}{{369.40}}\]

\(Percent\;change = 5.51\% \)