# 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}={6.3}frac{ ln{{C}}}{{C}_{{0}}} (b)the global temperature increase T by using T(R)=1.03R

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\ $R=6.3\frac{\mathrm{ln}C}{{C}_{0}}$
(b)the global temperature increase T by using T(R)=1.03R
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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 $R=k\frac{\mathrm{ln}C}{{C}_{0}}$, R is the radiative forcing in watts per square meter. Where ( is the preindustrial amount of carbon dioxide,
C is the current level of carbon dioxide.
And, according to IPCC, k = 6.3
(a) Let $R=6.3\mathrm{ln}{C}_{{C}_{0}}$
And given that, the carbon dioxide level = double the preindustrial amount of carbon dioxide
That is, $C=2{C}_{0}$
So, let $C=2{C}_{0}$
$R=63In2\frac{{C}_{0}}{{C}_{0}}$
Cancel ${C}_{0},R=6.3\mathrm{ln}2\frac{{C}_{0}}{{C}_{0}}$
$R=63\mathrm{ln}2$
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(R) = 1.03R
So, when $R=4.37,T\left(R\right)=1.03×4.37$
Therefore, T(R) = 4.50
Final statement:
Based on the given 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