Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 10

According to the recent studies, the average surface temperature of the earth has been rising steadily. Some scientist have modeled the temperature by the linear equation $T=0.02t + 8.50$, where $T$ is temperature in $^oC$ and $t$ represents years since 1900.



(a.) What do the slope and T-intercept represent?



$
\begin{equation}
\begin{aligned}
\boxed{ \begin{array}{l}
\text{The slope represents the increase of temperature as time increases. } \\
\text{Where the T intercept represents that the initial temperature in the year 1900 was 8.50.}
\end{array} }
\end{aligned}
\end{equation}
$



(b.) Predict the average global surface temperature in 2100 using the equation.



$t = 0$ represent years since 1900, and $t = 200$ represents 2100.



To solve for T, replace $t = 200$, we get:



$
\begin{equation}
\begin{aligned}
T &= 0.02 t + 8.50; \text{ where } t = 200\\
T &= 0.02(200) + 8.50\\
\end{aligned}
\end{equation}\\
\boxed{T = 12.5^0 C}
$