emancipezN

2021-08-14

To find:
a) radiative force R when the carbon dioxide level is double the preindustrial amount of carbon dioxide in watts per square meter by using $R=6.3In\frac{C}{{C}_{0}}$.
b) the global temperature increase T by using $T\left(R\right)=1.03R$

tabuordy

Concept:
Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model is $R=kIn\frac{C}{{C}_{0}}$, R is the radiative forcing in watts per square meter.
Where ${C}_{0}$ is the preindustrial amount of carbon dioxide,
C is the current level of carbon dioxide.
And, according to IPCC, $k=6.3$
a) Let $R=6.3In\frac{C}{{C}_{0}}$
And given that, the carbon dioxide level = double the preindustrial amount of carbon dioxide
That is, $C=2{C}_{0}$
So, let $C=2{C}_{0}$
$R=6.3In\frac{2{C}_{0}}{{C}_{0}}$
Cancel ${C}_{0},R=6.3In\frac{2{C}_{0}}{{C}_{0}}$
$R=6.3In2$
Using calculator, $R=6.3×0.6931$
$R=4.3668$
$R\approx 4.37$ watts per square meter.
Hence, radiative force R when the carbon dioxide level is double the preindustrial amount of carbon dioxide is 4.37 watts per square meter.
b) Let $R=4.37$ watts per square meter
And the global temperature increase $T\left(R\right)=1.03R$
So, when $R=4.37,T\left(R\right)=1.03×4.37$
Therefore, $T\left(R\right)=4.50$
Final statement:
Based on the function,
a) radiative force R when the carbon dioxide level is double the preindustrial amount of carbon dioxide is 4.37 watts per square meter.
b) the global temperature increase $T=4.50$.

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